# Erdős–Bacon number

A person's **Erdős–Bacon number** is the sum of one's Erdős number—which measures the "collaborative distance" in authoring academic papers between that person and Hungarian mathematician Paul Erdős—and one's Bacon number—which represents the number of links, through roles in films, by which the individual is separated from American actor Kevin Bacon.^{[1]}^{[2]} The lower the number, the closer a person is to Erdős and Bacon, which reflects a small world phenomenon in academia and entertainment.^{[3]}

The combined Erdős/Bacon number was introduced by mathematicians Tim Hsu and David Grabiner in 1999 or earlier; they pointed out that Daniel Kleitman has a combined number of 3: a Bacon number of 2 and Erdős number of 1.^{[4]}

To have a defined Erdős–Bacon number, it is necessary to have both appeared in a film and co-authored an academic paper, though it is not sufficient.

## Contents

## Scientists[edit]

Mathematician Daniel Kleitman has a combined number 3: he is a co-author of Erdős on multiple papers, and has a Bacon number of 2, via Minnie Driver in *Good Will Hunting*.^{[4]}

Astronomer Carl Sagan has an Erdős number of 4,^{[5]} via Steven J. Ostro, and a Bacon number of 2,^{[6]} for a total of 6. Physicist Richard Feynman has an Erdős number of 3^{[7]} and a Bacon number of 3, having appeared in the film *Anti-Clock* alongside Tony Tang.^{[8]}

Geneticist Jonathan Pritchard appeared in the 1998 movie *Without Limits*^{[9]} which gives him a Bacon number of 2.^{[10]} Pritchard has an Erdős number of 4^{[11]}^{[12]}^{[13]}^{[14]} thus giving him an Erdős–Bacon number of 6.

Theoretical physicist Stephen Hawking has an Erdős–Bacon number of 6: His Bacon number of 2 (via his appearance alongside John Cleese in *Monty Python Live (Mostly)* who acted alongside Kevin Bacon in *The Big Picture*) is lower than his Erdős number of 4.^{[15]}

## Actors[edit]

Canadian actor Albert M. Chan has an Erdős–Bacon number of 4. He co-authored a peer-reviewed paper on Orthogonal frequency-division multiplexing, giving him an Erdős number of 3,^{[16]}^{[17]}^{[18]} and was cast alongside Kevin Bacon in *Patriots Day*, giving him a Bacon number of 1.^{[19]}

Danica McKellar, who played Winnie Cooper in *The Wonder Years*, has an Erdős–Bacon number of 6, having coauthored a mathematics paper published while an undergraduate at the University of California, Los Angeles. Her paper gives her an Erdős number of 4, and she has a Bacon number of 2, both of them having worked with Margaret Easley.^{[2]}

Israeli-American actress Natalie Portman has an Erdős–Bacon number of 7. She collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird,^{[20]} who has a collaboration path^{[21]}^{[22]}^{[23]} leading to Joseph Gillis, who has an Erdős number of 1.^{[24]} Portman appeared in *A Powerful Noise Live* (2009) with Sarah Michelle Gellar, who appeared in *The Air I Breathe* (2007) with Bacon, giving Portman a Bacon number of 2 and an Erdős number of 5.

British actor Colin Firth has an Erdős–Bacon number of 7. Firth is credited as co-author of a neuroscience paper, "Political Orientations Are Correlated with Brain Structure in Young Adults",^{[25]} after he suggested on BBC Radio 4 that such a study could be done.^{[26]} Another author of that paper, Geraint Rees, has an Erdős number of 5,^{[27]}^{[28]}^{[29]} which gives Firth an Erdős number of 6. Firth's Bacon number of 1 is due to his appearance in *Where the Truth Lies*.^{[30]}

## Table[edit]

Name | Erdős number | Bacon number | Erdős–Bacon number |
---|---|---|---|

Behe, Michael J.Michael J. Behe | 4^{[31]} |
3^{[32]}^{[a]}^{[b]} |
7 |

Bialik, MayimMayim Bialik | 5^{[33]} |
2^{[33]} |
7 |

Billingsley, PatrickPatrick Billingsley | 4^{[34]}^{[35]}^{[36]}^{[37]} |
2^{[38]} |
6 |

Chan, Albert M.Albert M. Chan | 3^{[16]}^{[17]}^{[18]} |
1^{[19]} |
4 |

Dalrymple, DavidDavid Dalrymple | 3^{[39]}^{[40]}^{[41]} |
2^{[a]}^{[b]}^{[42]} |
5^{[a]}^{[b]} |

Dembski, William A.William A. Dembski | 4^{[43]}^{[44]}^{[45]}^{[46]} |
2^{[a]}^{[47]} |
6 |

Joel Fajans | 3^{[48]}^{[49]}^{[50]} |
2^{[51]}^{[52]}^{[53]} |
5^{[a]}^{[b]} |

Feynman, RichardRichard Feynman | 3^{[7]} |
3^{[8]} |
6 |

Hare, DonovanDonovan Hare | 2^{[54]}^{[55]} |
2^{[56]}^{[57]} |
4 |

Houh, HenryHenry Houh | 5^{[58]}^{[59]}^{[60]}^{[61]}^{[62]} |
2^{[63]}^{[64]} |
7 |

Knight, RobertRobert Knight | 4^{[65]}^{[66]}^{[67]}^{[68]} |
2^{[b]}^{[69]}^{[70]} |
6^{[b]} |

Mann, Michael E.Michael E. Mann | 5^{[71]} |
3^{[72]} |
8 |

Marks II, Robert J.Robert J. Marks II | 3^{[43]}^{[44]}^{[45]} |
2^{[73]}^{[74]}^{[75]} |
5 |

McKellar, DanicaDanica McKellar | 4^{[76]}^{[77]}^{[78]}^{[79]} |
2^{[c]} |
6 |

Metropolis, NicholasNicholas Metropolis | 2^{[80]} |
2^{[81]} |
4 |

Portman, NatalieNatalie Portman (Hershlag) | 5^{[20]}^{[21]}^{[22]}^{[23]}^{[24]} |
2^{[c]} |
7 |

Pritchard, JonathanJonathan Pritchard | 4^{[11]}^{[14]}^{[82]}^{[83]} |
2^{[9]}^{[10]} |
6 |

Sagan, CarlCarl Sagan | 4^{[7]} |
2^{[a]}^{[6]} |
6 |

Gonczarowski, YannaiYannai Gonczarowski | 2^{[84]} |
3^{[84]} |
5 |

Van Snellenberg, JaredJared Van Snellenberg | 4^{[85]}^{[86]}^{[87]}^{[88]} |
2^{[89]}^{[90]} |
6 |

Stern, TomerTomer Stern | 4^{[91]}^{[92]}^{[93]}^{[94]} |
3^{[95]}^{[96]}^{[97]} |
7 |

Strogatz, StevenSteven Strogatz | 3^{[98]}^{[99]}^{[100]} |
1^{[a]}^{[b]}^{[101]} |
4^{[a]}^{[b]} |

Chomsky, NoamNoam Chomsky | 4^{[102]}^{[103]}^{[104]}^{[105]} |
3^{[a]}^{[b]}^{[101]} |
7^{[a]}^{[b]} |

Chazelle, BernardBernard Chazelle | 2^{[106]}^{[107]} |
3^{[108]} |
5 |

Gyöngy, IstvánIstván Gyöngy | 3^{[109]}^{[110]}^{[111]} |
3^{[112]} |
6 |

Vidas, TimothyTimothy Vidas | 4 ^{[113]}^{[114]}^{[115]}^{[116]} |
3^{[a]}^{[b]}^{[117]}^{[118]}^{[119]} |
7 |

Zupan, AlexAlex Zupan | 5 ^{[120]}^{[121]}^{[122]}^{[123]} ^{[124]} |
3 ^{[125]}^{[126]}^{[127]} |
8 |

Goldberg, KenKen Goldberg | 3^{[128]}^{[129]}^{[130]} |
3^{[131]}^{[132]}^{[133]} |
6 |

Firth, ColinColin Firth | 5^{[25]} |
1^{[30]} |
6 |

Ken Ono | 2^{[134]} |
2^{[135]} |
4^{[135]} |

Mulliner, CollinCollin Mulliner | 4^{[136]} |
4^{[136]} |
8 |

Notes:

## References[edit]

**^**Singh, Simon (May 1, 2002). "And the winner tonight is".*The Telegraph*. Archived from the original on November 12, 2012. Retrieved September 26, 2013.- ^
^{a}^{b}"There's not much separating her from Bacon, Erdos".*USA Today*. August 14, 2007. Archived from the original on November 4, 2012. **^**Collins, James J.; Chow, Carson C. (1998). "It's a small world".*Nature*.**393**(6684): 409–10. doi:10.1038/30835. PMID 9623993.- ^
^{a}^{b}The Erdős Number Project at the Wayback Machine (archived 3 February 1999); current version at "Erdös Number Project". Oakland University. **^**"The Erdős Number Project, Paths to Erdős". Archived from the original on October 28, 2008. Retrieved 2009-10-27.- ^
^{a}^{b}"The Oracle of Bacon at Virginia". Retrieved 2013-01-22.^{[self-published source?]} - ^
^{a}^{b}^{c}"The Erdős Number Project, Paths to Erdős". Archived from the original on 2006-11-07. Retrieved 2006-12-01. - ^
^{a}^{b}"The Oracle of Bacon at Virginia". Retrieved 2006-12-05.^{[self-published source?]} - ^
^{a}^{b}*Without Limits*on IMDb as David Bedford, the English distance runner, in the 1972 Munich Olympics - ^
^{a}^{b}*Animal House*on IMDb with Donald Southerland who portrayed Bill Bowerman in Without Limits and Kevin Bacon - ^
^{a}^{b}Pritchard, Jonathan K.; Seielstad, Mark T.; Perez-Lezaun, Anna; Feldman, Marcus W. (1999). "Population Growth of Human Y. Chromosomes: A Study of Y Chromosome Microsatellites".*Molecular Biology and Evolution*.**16**(12): 1791–1798. doi:10.1093/oxfordjournals.molbev.a026091. PMID 10605120. **^**Feldman, Marcus W.; Karlin, Samuel (1971). "The Evolution of Biology: A direct approach through the theory of linkage and selection".*Theoretical Population Biology*.**2**(4): 482–492. doi:10.1016/0040-5809(71)90036-0.**^**Karlin, Samuel; Szegö, Gábor (1960). "On certain determinants whose elements are orthogonal polynomials".*Journal d’Analyse Mathématique*.**8**(1): 1–157. doi:10.1007/bf02786848.- ^
^{a}^{b}Erdős, Paul; Szegö, Gábor (1942). "On a Problem of I. Schur".*Annals of Mathematics*.**43**: 451–470. doi:10.2307/1968803. **^**Some Famous People with Finite Erdös Numbers- ^
^{a}^{b}Lee, Inkyu; Chan, Albert M.; Sundberg, Carl-Erik (2004). "Space-time bit-interleaved coded modulation for OFDM systems".*IEEE Transactions on Signal Processing*.**52**(3): 820–25. doi:10.1109/TSP.2003.822350. - ^
^{a}^{b}Duren, Peter; Khavinson, Dmitry; Shapiro, Harold S.; Sundberg, Carl-Erik (1994). "Invariant subspaces in Bergman spaces and the biharmonic equation".*Michigan Mathematical Journal*.**41**(2): 247–59. doi:10.1307/mmj/1029004992. - ^
^{a}^{b}Erdős, Paul; Shapiro, Harold S. (1965). "Large and small subspaces of Hilbert space".*Michigan Mathematical Journal*.**12**(2): 169–78. doi:10.1307/mmj/1028999306. - ^
^{a}^{b}*Patriots Day*on IMDb as "Computer Forensic Tech" - ^
^{a}^{b}Baird, A; Kagan, J; Gaudette, T; Walz, KA; Hershlag, N; Boas, DA (2002). "Frontal Lobe Activation during Object Permanence: Data from Near-Infrared Spectroscopy".*NeuroImage*.**16**(4): 1120–5. doi:10.1006/nimg.2002.1170. PMID 12202098. - ^
^{a}^{b}Baird, Abigail A.; Colvin, Mary K.; Vanhorn, John D.; Inati, Souheil; Gazzaniga, Michael S. (2005). "Functional Connectivity: Integrating Behavioral, Diffusion Tensor Imaging, and Functional Magnetic Resonance Imaging Data Sets".*Journal of Cognitive Neuroscience*.**17**(4): 687–93. doi:10.1162/0898929053467569. PMID 15829087. - ^
^{a}^{b}Victor, Jonathan D.; Maiese, Kenneth; Shapley, Robert; Sidtis, John; Gazzaniga, Michael S. (1989). "Acquired central dyschromatopsia: analysis of a case with preservation of color discrimination".*Clinical Vision Sciences*.**4**: 183–96. - ^
^{a}^{b}Azor, Ruth; Gillis, J.; Victor, J. D. (1982). "Combinatorial Applications of Hermite Polynomials".*SIAM Journal on Mathematical Analysis*.**13**(5): 879–90. doi:10.1137/0513062. - ^
^{a}^{b}Erdos, P.; Gillis, J. (2009). "Note on the Transfinite Diameter".*Journal of the London Mathematical Society*. s1-12 (3): 185. doi:10.1112/jlms/s1-12.2.185. - ^
^{a}^{b}Kanai, Ryota; Feilden, Tom; Firth, Colin; Rees, Geraint (2011). "Political Orientations Are Correlated with Brain Structure in Young Adults".*Current Biology*.**21**(8): 677–80. doi:10.1016/j.cub.2011.03.017. PMC 3092984 . PMID 21474316. **^**"Colin Firth credited in brain research".*BBC News*. 2011-06-05.**^**Schwarzkopf, Dietrich Samuel; Schindler, Andreas; Rees, Geraint (2010). Baker, Chris I, ed. "Knowing with Which Eye We See: Utrocular Discrimination and Eye-Specific Signals in Human Visual Cortex".*PLoS ONE*.**5**(10): e13775. doi:10.1371/journal.pone.0013775. PMC 2966441 . PMID 21048942.**^**"Andreas Schindler". Max Planck Institutefor Biological Cybernetics. Retrieved December 29, 2011.**^**"Can I help you find your Erdos number?". users.med.cornell.edu. Retrieved December 29, 2011.^{[self-published source?]}- ^
^{a}^{b}*Where the Truth Lies*on IMDb **^**Marks Ii, Robert J; Behe, Michael J; Dembski, William A; Gordon, Bruce L; Sanford, John C (2013).*Biological Information*. doi:10.1142/8818. ISBN 978-981-4508-71-1.^{[page needed]}**^***Unlocking the Mystery of Life*on IMDb^{[not in citation given]}- ^
^{a}^{b}"Erdős Bacon Sabbath Project › Mayim Bialik". Retrieved 2014-02-09. **^**Baum, Leonard E.; Billingsley, Patrick (1965). "Asymptotic Distributions for the Coupon Collector's Problem".*The Annals of Mathematical Statistics*.**36**(6): 1835–9. doi:10.1214/aoms/1177699813. JSTOR 2239126.**^**Baum, Leonard E; Herzberg, Norman P; Lomonaco, S.J; Sweet, Melvin M (1977). "Fields of almost periodic sequences".*Journal of Combinatorial Theory, Series A*.**22**(2): 169–80. doi:10.1016/0097-3165(77)90049-8.**^**Conway, J.H.; Lomonaco, S.J.; Sloane, N.J.A. (1990). "A [45,13] code with minimal distance 16".*Discrete Mathematics*.**83**(2–3): 213–7. doi:10.1016/0012-365X(90)90007-5.**^**Conway, J. H.; Croft, H. T.; Erdos, P.; Guy, M. J. T. (1979). "On the Distribution of Values of Angles Determined by Coplanar Points".*Journal of the London Mathematical Society*. s2-19 (1): 137–43. doi:10.1112/jlms/s2-19.1.137.**^**Pat Billingsley at the Oracle of Bacon^{[self-published source?]}**^**Gershenfeld, Neil; Dalrymple, David; Chen, Kailiang; Knaian, Ara; Green, Forrest; Demaine, Erik D.; Greenwald, Scott; Schmidt-Nielsen, Peter (2010). "Reconfigurable asynchronous logic automata".*Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '10*. pp. 1–6. doi:10.1145/1706299.1706301. ISBN 978-1-60558-479-9.**^**Alon, Noga; Bădoiu, Mihai; Demaine, Erik D.; Farach-Colton, Martin; Hajiaghayi, Mohammadtaghi; Sidiropoulos, Anastasios (2008). "Ordinal embeddings of minimum relaxation".*ACM Transactions on Algorithms*.**4**(4): 1–21. doi:10.1145/1383369.1383377.**^**Alon, Noga; Erdös, P. (1985). "An Application of Graph Theory to Additive Number Theory".*European Journal of Combinatorics*.**6**(3): 201–3. doi:10.1016/S0195-6698(85)80027-5.**^**"David Dalrymple's Kevin Bacon number". The Oracle of Bacon. Retrieved 2012-07-24.^{[self-published source?]}- ^
^{a}^{b}Wunsch Ii, Donald C.; Marks Ii, Robert J.; Caudell, Thomas P.; Capps, C. David (1992). "Limitations of a class of binary phase-only filters".*Applied Optics*.**31**(26): 5681–7. doi:10.1364/AO.31.005681. PMID 20733753. and Wunsch, D.C.; Caudell, T.P.; Capps, C.D.; Marks, R.J.; Falk, R.A. (1993). "An optoelectronic implementation of the adaptive resonance neural network".*IEEE Transactions on Neural Networks*.**4**(4): 673–84. doi:10.1109/72.238321. PMID 18267767. - ^
^{a}^{b}Harary, Frank; Lim, Meng-Hiot; Agarwal ‡, Amit; Wunsch §, Donald C. (2004). "Algorithms for derivation of structurally stable Hamiltonian signed graphs".*International Journal of Computer Mathematics*.**81**(11): 1349–56. doi:10.1080/0020716042000261432. - ^
^{a}^{b}Erdös, Paul; Harary, Frank; Tutte, William T. (2010). "On the dimension of a graph".*Mathematika*.**12**(2): 118–22. doi:10.1112/S0025579300005222. and Erdös, Paul; Harary, Frank; Klawe, Maria (1980). "Residually-Complete Graphs".*Combinatorial Mathematics, Optimal Designs and Their Applications*. Annals of Discrete Mathematics.**6**. pp. 117–23. doi:10.1016/S0167-5060(08)70698-8. ISBN 978-0-444-86048-4. **^**Dembski, William A.; Marks Ii, Robert J. (2009). "Conservation of Information in Search: Measuring the Cost of Success".*IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans*.**39**(5): 1051–61. doi:10.1109/TSMCA.2009.2025027.**^**William Dembski on IMDb^{[not in citation given]}**^**McCarthy, J. E.; Yu. Backhaus, E.; Fajans, J. (1998-11-18). "Solving Poisson's equation with interior conditions".*Journal of Mathematical Physics*.**39**(12): 6720–6729. doi:10.1063/1.532653. ISSN 0022-2488.**^**Krantz, Steven G.; McCarthy, John E.; Parks, Harold R. "Geometric characterizations of centroids of simplices".*Journal of Mathematical Analysis and Applications*.**316**(1): 87–109. doi:10.1016/j.jmaa.2005.04.046.**^**Erdös, P.; Godsil, C.D.; Krantz, S.G.; Parsons, T.D. "Intersection Graphs for Families of Balls in Rn".*European Journal of Combinatorics*.**9**(5): 501–505. doi:10.1016/s0195-6698(88)80007-6.**^**"Joel Fajans".*IMDb*. Retrieved 2017-10-11.**^***Through the Wormhole (TV Series 2010– )*, retrieved 2017-10-11**^***Eastwood Directs: The Untold Story (2013)*, retrieved 2017-10-11**^**Abbott, H. L.; Hare, D. R. "Sparse color-critical hypergraphs".*Combinatorica*.**9**(3): 233–243. doi:10.1007/BF02125892. ISSN 0209-9683.**^**Abbott, H. L.; Erdos, P.; Hanson, D. (1 January 1974). "On the Number of Times an Integer Occurs as a Binomial Coefficient".*The American Mathematical Monthly*.**81**(3): 256–261. doi:10.2307/2319526. JSTOR 2319526.**^**"Donovan Hare".*IMDb*. played Donovan Brady in "One Man".*IMDb*. 1 July 1979. with "Terrence Labrosse".*IMDb*.**^**"Terrence Labrosse".*IMDb*. was in "Criminal Law". 28 April 1989. with Kevin Bacon**^**Houh, H.H.; Adam, J.F.; Ismert, M.; Lindblad, C.J.; Tennenhouse, D.L. (1995). "The VuNet desk area network: Architecture, implementation, and experience".*IEEE Journal on Selected Areas in Communications*.**13**(4): 710–21. doi:10.1109/49.382161.**^**Tennenhouse, David; Lampson, Butler; Gillett, Sharon Eisner; Klein, Jennifer Steiner (1996). "Virtual infrastructure: Putting information infrastructure on the technology curve".*Computer Networks and ISDN Systems*.**28**(13): 1769–90. doi:10.1016/0169-7552(96)00009-8.**^**C Ellison, B Frantz, B Lampson, R Rivest, B Thomas, T Ylonen, "SPKI Certificate Theory", IETF Network Working Group RFC2693, September 1999**^**Rivest, R.L.; Meyer, A.R.; Kleitman, D.J.; Winklmann, K.; Spencer, J. (1980). "Coping with errors in binary search procedures".*Journal of Computer and System Sciences*.**20**(3): 396–404. doi:10.1016/0022-0000(80)90014-8.**^**Erdös, Paul; Kleitman, Daniel J. (1968). "On coloring graphs to maximize the proportion of multicolored k-edges".*Journal of Combinatorial Theory*.**5**(2): 164–9. doi:10.1016/S0021-9800(68)80051-1.**^***21*on IMDb as "Chinatown Dealer" with line "Winner winner chicken dinner"^{[not in citation given]}**^***Quicksilver*on IMDb with Laurence Fishburne from 21 appearing with Kevin Bacon^{[not in citation given]}**^**Chang, Edward F.; Edwards, Erik; Nagarajan, Srikantan S.; Fogelson, Noa; Dalal, Sarang S.; Canolty, Ryan T.; Kirsch, Heidi E.; Barbaro, Nicholas M.; Knight, Robert T. (2011). "Cortical Spatio-temporal Dynamics Underlying Phonological Target Detection in Humans".*Journal of Cognitive Neuroscience*.**23**(6): 1437–46. doi:10.1162/jocn.2010.21466. PMC 3895406 . PMID 20465359.**^**Dalal, S.S.; Baillet, S.; Adam, C.; Ducorps, A.; Schwartz, D.; Jerbi, K.; Bertrand, O.; Garnero, L.; Martinerie, J.; Lachaux, J.P. (2009). "MEG reconstructions of gamma band modulations during attentive reading validated by simultaneous intracranial EEG".*NeuroImage*.**47**: S162. doi:10.1016/S1053-8119(09)71718-5.**^**Raiter, Y; Farfel, A; Lehavi, O; Goren, O B; Shamiss, A; Priel, Z; Koren, I; Davidson, B; Schwartz, D; Goldberg, A; Bar-Dayan, Y (2008). "Mass casualty incident management, triage, injury distribution of casualties and rate of arrival of casualties at the hospitals: Lessons from a suicide bomber attack in downtown Tel Aviv".*Emergency Medicine Journal*.**25**(4): 225–9. doi:10.1136/emj.2007.052399. PMID 18356360.**^**Erdös, P.; Koren, I.; Moran, S.; Silberman, G. M.; Zaks, S. (1988). "Minimum-diameter cyclic arrangements in mapping data-flow graphs onto VLSI arrays".*Mathematical Systems Theory*.**21**: 85–98. doi:10.1007/BF02088008.**^***Number One with a Bullet*on IMDb as Himself^{[not in citation given]}**^***The Woodsman*on IMDb with Mos Def from Number One With A Bullet appearing with Kevin Bacon^{[not in citation given]}**^**Michael E. Mann at MathSciNet**^**Michael E. Mann at the Oracle of Bacon**^**Robert J. Marks II on IMDb**^**Robert J. Marks II in "Expelled: No Intelligence Allowed" with Ben Stein on IMDb**^**Ben Stein and Kevin Bacon in "Planes, Trains and Automobiles" on IMDb**^**"The Erdős Number Project, Erdos1". Archived from the original on 2006-12-07. Retrieved 2006-12-20.**^**Chayes, L; McKellar, D; Winn, B (1998). "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on".*Journal of Physics A: Mathematical and General*.**31**(45): 9055. doi:10.1088/0305-4470/31/45/005.**^**Chayes, J. T.; Chayes, L.; Kotecký, R. (1995). "The analysis of the Widom-Rowlinson model by stochastic geometric methods".*Communications in Mathematical Physics*.**172**(3): 551. doi:10.1007/BF02101808.**^**Kotecký, R.; Preiss, D. (1986). "Cluster expansion for abstract polymer models".*Communications in Mathematical Physics*.**103**(3): 491–8. doi:10.1007/BF01211762.**^**"Erdős Bacon Sabbath Project › Richard Feynman". Retrieved 2015-12-25.**^**Nicholas Metropolis at the Oracle of Bacon**^**Feldman, Marcus W.; Karlin, Samuel (1971). "The Evolution of Biology: A direct approach through the theory of linkage and selection".*Theoretical Population Biology*.**2**(4): 482–492. doi:10.1016/0040-5809(71)90036-0.**^**Karlin, Samuel; Szegö, Gábor (1960). "On certain determinants whose elements are orthogonal polynomials".*Journal d’Analyse Mathématique*.**8**(1): 1–157. doi:10.1007/bf02786848.- ^
^{a}^{b}"Yannai Gonczarowski's website".^{[self-published source?]} **^**Wager, Tor D.; Lindquist, Martin A.; Nichols, Thomas E.; Kober, Hedy; Snellenberg, Jared X. Van. "Evaluating the consistency and specificity of neuroimaging data using meta-analysis".*NeuroImage*.**45**(1): S210–S221. doi:10.1016/j.neuroimage.2008.10.061.**^**Lindquist, M. A.; Zhang, Cun-Hui; Glover, G.; Shepp, L.; Yang, Q. X. (September 2006). "A generalization of the two-dimensional prolate spheroidal wave function method for nonrectilinear MRI data acquisition methods".*IEEE Transactions on Image Processing*.**15**(9): 2792–2804. doi:10.1109/tip.2006.877314. ISSN 1057-7149.**^**Chen, Robert W.; Shepp, Larry A.; Yao, Yi-Ching; Zhang, Cun-Hui. "On Optimality of Bold Play for Primitive Casinos in the Presence of Inflation".*Journal of Applied Probability*.**42**(01): 121–137. doi:10.1017/s0021900200000103.**^**Erdös, Paul; Chen, Robert W. "Random walks on Z2n".*Journal of Multivariate Analysis*.**25**(1): 111–118. doi:10.1016/0047-259x(88)90156-x.**^***Agent Cody Banks (2003)*, retrieved 2017-08-05. Jared Van Snellenberg played "Earl's Intern." Frankie Muniz played "Cody Banks."**^***My Dog Skip (2000)*, retrieved 2017-08-05. Starring Kevin Bacon and Frankie Muniz.**^**Wasserstrom, Adam; Frumkin, Dan; Adar, Rivka; Itzkovitz, Shalev; Stern, Tomer; Kaplan, Shai; Shefer, Gabi; Shur, Irena; Zangi, Lior; Reizel, Yitzhak; Harmelin, Alon; Dor, Yuval; Dekel, Nava; Reisner, Yair; Benayahu, Dafna; Tzahor, Eldad; Segal, Eran; Shapiro, Ehud (2008). Bourne, Philip E, ed. "Estimating Cell Depth from Somatic Mutations".*PLoS Computational Biology*.**4**(5): e1000058. doi:10.1371/journal.pcbi.1000058. PMC 2275312 . PMID 18404205.**^**Frumkin, Dan; Wasserstrom, Adam; Kaplan, Shai; Feige, Uriel; Shapiro, Ehud (2005). "Genomic Variability within an Organism Exposes Its Cell Lineage Tree".*PLoS Computational Biology*.**1**(5): e50. doi:10.1371/journal.pcbi.0010050. PMC 1274291 . PMID 16261192.**^**Feige, Uriel; Goldwasser, Shafi; Lovász, Laszlo; Safra, Shmuel; Szegedy, Mario (1996). "Interactive proofs and the hardness of approximating cliques".*Journal of the ACM*.**43**(2): 268–92. doi:10.1145/226643.226652.**^**On the graph of large distance (1989)^{[page needed]}**^***Etz Hadomim Tafus*on IMDb^{[not in citation given]}**^***Every Time We Say Goodbye*on IMDb^{[not in citation given]}**^***Apollo 13*on IMDb^{[not in citation given]}**^**Stone, H. A.; Nadim, Ali; Strogatz, Steven H. (2006). "Chaotic streamlines inside drops immersed in steady Stokes flows".*Journal of Fluid Mechanics*.**232**: 629–46. doi:10.1017/S002211209100383X.**^**Limon, Alfonso; Bertuglia, Silvia; Nadim, Ali; Salamon, Peter (2006). "Oxygen transport from the outer boundary of a pulsating wall of an arteriole".*Mathematics and Computers in Simulation*.**73**(1–4): 175–82. doi:10.1016/j.matcom.2006.06.002.**^**Salamon, Peter; Erdős, Paul (1988). "The solution to a problem of Grünbaum".*Canadian Mathematical Bulletin*.**31**(2): 129–38. doi:10.4153/CMB-1988-020-2.- ^
^{a}^{b}*Connected: The Power of Six Degrees*on IMDb **^**Chomsky, N.; Schützenberger, M.P. (1963). "The Algebraic Theory of Context-Free Languages".*Computer Programming and Formal Systems*. Studies in Logic and the Foundations of Mathematics.**35**. pp. 118–61. doi:10.1016/S0049-237X(08)72023-8. ISBN 978-0-444-53400-2.**^**Berge, Claude; Schützenberger, Marcel Paul (1956). "Jeux de Nim et solutions".*C. R. Acad. Sci. Paris*(in French).**242**: 1672–4.**^**Berge, C.; Simonovits, M. (1974). "The coloring numbers of the direct product of two hypergraphs".*Hypergraph Seminar*. Lecture Notes in Mathematics.**411**. pp. 21–33. doi:10.1007/BFb0066176. ISBN 978-3-540-06846-4.**^**Erdős, P.; Simonovits, M. (1966). "A limit theorem in graph theory".*Studia Sci. Math. Hungar*.**1**: 51–7.**^**Brönnimann, Hervé; Chazelle, Bernard; Pach, János (1993). "How hard is half-space range searching?".*Discrete & Computational Geometry*.**10**: 143–55. doi:10.1007/BF02573971.**^**Erdős, P.; Pach, J. (1980). "On a problem of L. Fejes Tóth".*Discrete Mathematics*.**30**(2): 103–9. doi:10.1016/0012-365X(80)90111-9.**^**Bernard Chazelle at the Oracle of Bacon**^**Gyöngy, István; Michaletzky, György (2004). "On Wong–Zakai approximations with δ–martingales".*Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences*.**460**: 309–324. doi:10.1098/rspa.2003.1244.**^**Michaletzky, György; Gerencsér, László (2002). "BIBO stability of linear switching systems".*Institute of Electrical and Electronics Engineers. Transactions on Automatic Control*.**47**: 1895–1898. doi:10.1109/TAC.2002.804470.**^**Erdős, Pál; Gerencsér, László; Máté, Attila (1970). "Problems of graph theory concerning optimal design".*Combinatorial theory and its applications, I (Proc. Colloq., Balatonfüred, 1969)*: 317–325.**^**István Gyöngy at the Oracle of Bacon**^**Vidas, Timothy; Nicolas, Christin; Cranor, Lorrie (2011). "Curbing Android Permission Creep".*Proceedings of IEEE W2SP*. Retrieved 28 January 2016.**^**Cranor, Lorrie; Wright, Rebecca (2000). "Influencing software usage".*Proceedings of the tenth ACM conference on Computers, freedom and privacy*: 44–55. doi:10.1145/332186.332210. Retrieved 28 January 2016.**^**Alon, Noga; Merritt, Michael; Reingold, Omer; Taubenfeld, Gadi; Wright, Rebecca (2005). "Tight bounds for shared memory systems accessed by Byzantine processes".*Distributed Computing*.**18**(2): 99–109. doi:10.1007/s00446-005-0125-8. Retrieved 28 January 2016.**^**Alon, Noga; Erdos, Paul (1989). "Disjoint edges in geometric graphs".*Discrete & Computational Geometry*.**4**(1): 287–290. doi:10.1007/BF02187731. Retrieved 28 January 2016.**^***DEFCON: The Documentary*on IMDb**^***Ocean's Thirteen*on IMDb**^***Lemon Sky*on IMDb**^**Blackburn, Chantel C.; Lund, Kristina; Schlicker, Steven; Sigmon, Patrick; Zupan, Alexander (March 2009). "A Missing Prime Configuration in the Hausdorff Metric Geometry".*Journal of Geometry*.**92**(1): 28–59.**^**Dickinson, William C.; Lund, Kristina (October 2006). "The volume principal".*Mathematics Magazine*.**79**(4): 251–261.**^**Connelly, Robert; Dickinson, William (2013). "Periodic planar disc packings".*Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences*.**372**(2008). doi:10.1098/rsta.2012.0039. ISSN 1364-503X.**^**Bailey, R. A.; Cameron, Peter J.; Connelly, Robert (2008). "Sudoku, gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes".*Amer. Math. Monthly*.**115**(5): 383–404.**^**Cameron, P. J; Erdős, P (1990), "On the number of sets of integers with various properties",*Number theory (Banff, AB, 1988)*, Berlin: de Gruyter, pp. 61–79**^***Loves of a cyclops*on IMDb**^***Last Weekend*on IMDb**^***Starting Over*on IMDb**^**Aronov, B.; Erdős, P.; Goddard, W.; Kleitman, D. J.; Klugerman, M.; Pach, J.; Schulman, L. J. (1994-06-01). "Crossing families".*Combinatorica*.**14**(2): 127–134. doi:10.1007/BF01215345. ISSN 0209-9683.**^**Aronov, B.; Berg, M. de; Stappen, A. F. van der; Švestka, P.; Vleugels, and J. (1999-12-01). "Motion Planning for Multiple Robots".*Discrete & Computational Geometry*.**22**(4): 505–525. doi:10.1007/PL00009476. ISSN 0179-5376.**^**Berretty, Robert-Paul; Goldberg, Ken; Overmars, Mark H.; van der Stappen, A. Frank (2001-11-01). "Trap Design for Vibratory Bowl Feeders".*The International Journal of Robotics Research*.**20**(11): 891–908. doi:10.1177/02783640122068173. ISSN 0278-3649.**^***She's Having a Baby (1988)*, retrieved 2017-08-11**^***Earth and the American Dream (1992)*, retrieved 2017-08-11**^***Connected: An Autoblogography About Love, Death & Technology (2011)*, retrieved 2017-08-11**^**"List of people by Erdős number".*Wikipedia*. 2017-12-09.- ^
^{a}^{b}Salerno, Adriana (2014-09-01). "The Man Who Knew The Man Who Knew Infinity".*PhD + epsilon*. Retrieved 2017-12-27. - ^
^{a}^{b}"Collin Mulliner's website".^{[self-published source?]}