Proof of Conway's lost cosmological theorem

Authors:
Shalosh B. Ekhad and Doron Zeilberger

Journal:
Electron. Res. Announc. Amer. Math. Soc. **3** (1997), 78-82

MSC (1991):
Primary 05Axx

DOI:
https://doi.org/10.1090/S1079-6762-97-00026-7

Published electronically:
August 21, 1997

Accompanying material:
Maple Program

Accompanying material:
Program input file

Accompanying material:
Program output file

MathSciNet review:
1461977

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: John Horton Conway's Cosmological Theorem about sequences like **1, 11, 21, 1211, 111221, 312211,...**, for which no extant proof existed, is given a new proof, this time hopefully for good.

**[AHK]**K. Appel and W. Haken,*Every planar map is four colorable. I. Discharging*, Illinois J. Math.**21**(1977), no. 3, 429–490. MR**0543792**

K. Appel, W. Haken, and J. Koch,*Every planar map is four colorable. II. Reducibility*, Illinois J. Math.**21**(1977), no. 3, 491–567. MR**0543793**

K. Appel and W. Haken,*The class check lists corresponding to the supplement: “Every planar map is four colorable. I. Discharging” (Illinois J. Math. 21 (1977), no. 3, 429–490)*, Illinois J. Math.**21**(1977), no. 3, C1-C210. (microfiche supplement). MR**0543794**

K. Appel and W. Haken,*Supplement to: “Every planar map is four colorable. I. Discharging” (Illinois J. Math. 21 (1977), no. 3, 429–490) by Appel and Haken; “II. Reducibility” (ibid. 21 (1977), no. 3, 491–567) by Appel, Haken and J. Koch*, Illinois J. Math.**21**(1977), no. 3, 1–251. (microfiche supplement). MR**0543795**

Kenneth Appel and Wolfgang Haken,*The solution of the four-color-map problem*, Sci. Amer.**237**(1977), no. 4, 108–121, 152. MR**0543796**, https://doi.org/10.1038/scientificamerican1077-108

Kenneth Appel and Wolfgang Haken,*Every planar map is four colorable*, J. Recreational Math.**9**(1976/77), no. 3, 161–169. MR**0543797**

K. Appel and W. Haken,*Every planar map is four colorable. I. Discharging*, Illinois J. Math.**21**(1977), no. 3, 429–490. MR**0543792**

K. Appel, W. Haken, and J. Koch,*Every planar map is four colorable. II. Reducibility*, Illinois J. Math.**21**(1977), no. 3, 491–567. MR**0543793**

K. Appel and W. Haken,*The class check lists corresponding to the supplement: “Every planar map is four colorable. I. Discharging” (Illinois J. Math. 21 (1977), no. 3, 429–490)*, Illinois J. Math.**21**(1977), no. 3, C1-C210. (microfiche supplement). MR**0543794**

K. Appel and W. Haken,*Supplement to: “Every planar map is four colorable. I. Discharging” (Illinois J. Math. 21 (1977), no. 3, 429–490) by Appel and Haken; “II. Reducibility” (ibid. 21 (1977), no. 3, 491–567) by Appel, Haken and J. Koch*, Illinois J. Math.**21**(1977), no. 3, 1–251. (microfiche supplement). MR**0543795**

Kenneth Appel and Wolfgang Haken,*The solution of the four-color-map problem*, Sci. Amer.**237**(1977), no. 4, 108–121, 152. MR**0543796**, https://doi.org/10.1038/scientificamerican1077-108

Kenneth Appel and Wolfgang Haken,*Every planar map is four colorable*, J. Recreational Math.**9**(1976/77), no. 3, 161–169. MR**0543797****[C]**Thomas M. Cover and B. Gopinath (eds.),*Open problems in communication and computation*, Springer-Verlag, New York, 1987. MR**922073****[CG]**J. H. Conway and R. K. Guy,*The book of numbers*, Copernicus, New York, 1996. CMP**97:02****[F]**S. Finch,*Favorite Mathematical Constants Website*.**[RSST]**N. Robertson, D. P. Sanders, P. Seymour, and R. Thomas,*A new proof of The Four-Color Theorem*, ERA Amer. Math. Soc.**2**(1996), 17-25.**[SP]**N. J. A. Sloane and Simon Plouffe,*The encyclopedia of integer sequences*, Academic Press, Inc., San Diego, CA, 1995. With a separately available computer disk. MR**1327059****[V]**Ilan Vardi,*Computational recreations in Mathematica*, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1991. MR**1150054**

Retrieve articles in *Electronic Research Announcements of the American Mathematical Society*
with MSC (1991):
05Axx

Retrieve articles in all journals with MSC (1991): 05Axx

Additional Information

**Shalosh B. Ekhad**

Affiliation:
Department of Mathematics, Temple University, Philadelphia, PA 19122

Email:
ekhad@math.temple.edu

**Doron Zeilberger**

Affiliation:
Department of Mathematics, Temple University, Philadelphia, PA 19122

Email:
zeilberg@math.temple.edu

DOI:
https://doi.org/10.1090/S1079-6762-97-00026-7

Received by editor(s):
May 6, 1997

Published electronically:
August 21, 1997

Additional Notes:
Supported in part by the NSF

Communicated by:
Ronald Graham

Article copyright:
© Copyright 1997
American Mathematical Society