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 (Added Nov. 30, 2003: it just got published in INTEGERS ) by Steven Byrnes.

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

The input yields the output

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