Chomp, Recurrences, and Chaos(?)
By Doron Zeilberger
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Appeared in J. Difference Equations and its Applications 10(2004), 1281-1293, (special issue in honor of Saber Elaydi).

Written: June 3, 2003.

Last Update : June 9, 2003.

Last Update of this page (adding confirming data to a conjecture of Craig Larson (see below)): June 5, 2015.

This paper, a sequel to 3-Rowed Chomp is an excercise in `computer-generated' research, using `Ultimately-Periodic Sequences' as the ansatz.

It was inspired by previous work of my student Xinyu Sun, who made a very interesting `periodicity conjecture' and by its brilliant proof (paper G3 in INTEGERS vol. 3) by Steven Byrnes (current homepage, viewed June 5, 2015).

This paper is dedicated with friendship and admiration to Difference Equation and Chaos Guru Saber Elaydi.

IMPORTANT: This article is accompanied by the Maple package BYRNES. You should also have the pre-computed data file ChompData, in the same directory.

ChompData contains three lists: ChompLosers400 describing the ultimately-periodic sequences B_c for 0<=c<=400, Grundy100_3, and Grundy50_6, for the positions with Grundy value <=3 and c<=100 and Grundy value<=6 and c<=50 respectively.

Added June 5, 2015: To see confirming data for a conjecture of Craig Larson and his amazing program CONJECTURING (written by Nico Van Cleemput and Larson).

The input yields the output

Added June 11, 2015: Craig Larson, and Bryan Kaperick, an undergrad from Virginia Tech, found a very elegant proof of this conjecture.

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