Chomp, recurrences and Chaos(?)

Research output: Contribution to journalArticle

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Abstract

In this article, dedicated with admiration and friendship to chaos and difference (and hence recurrence) equations guru Saber Elaydi, I give a new approach and a new algorithm for Chomp, David Gale's celebrated combinatorial game. This work is inspired by Xinyu Sun's "ultimate-periodicity" conjecture and by its brilliant proof by highschool student Steven Byrnes. The algorithm is implemented in a Maple package BYRNES accompanying this article. By looking at the output, and inspired by previous work of Andries Brouwer, I speculate that Chomp is chaotic, in a yet-to-be-made-precise sense, because the losing positions are given by "weird" recurrences.

Original languageEnglish (US)
Pages (from-to)1281-1293
Number of pages13
JournalJournal of Difference Equations and Applications
Volume10
Issue number13-15
DOIs
StatePublished - Nov 1 2004

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Keywords

  • Chaos
  • Chomp
  • Difference equations
  • Recurrence equations

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