Using the "freshman's dream" to prove combinatorial congruences

Moa Apagodu, Doron Zeilberger

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Recently, William Y.C. Chen, Qing-Hu Hou, and Doron Zeilberger developed an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequences, namely those (like the Catalan and Motzkin sequences) that are expressible in terms of constant terms of powers of Laurent polynomials. We first give a leisurely exposition of their approach and then extend it in two directions. The Laurent polynomials may be of several variables, and instead of single sums we have multiple sums. In fact, we even combine these two generalizations. We conclude with some super-challenges.

Original languageEnglish (US)
Pages (from-to)597-608
Number of pages12
JournalAmerican Mathematical Monthly
Volume124
Issue number7
DOIs
StatePublished - Aug 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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