Congruences for Catalan and Motzkin numbers and related sequences

2004/07/19 by Emeric Deutsch, Deutsch, Emeric, Bruce E. Sagan +1 · 1 citation
Mathematics · #05A10 (Primary) 11A07 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A10 #msc:11A07

paper · pdf · doi:10.48550/arxiv.math/0407326

22 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan

arxiv created 2004/07/19 · arxiv updated 2009/12/01

Abstract

We prove various congruences for Catalan and Motzkin numbers as well as related sequences. The common thread is that all these sequences can be expressed in terms of binomial coefficients. Our techniques are combinatorial and algebraic: group actions, induction, and Lucas' congruence for binomial coefficients come into play. A number of our results settle conjectures of Benoit Cloitre and Reinhard Zumkeller. The Thue-Morse sequence appears in several contexts.

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• Galois Groups of Apéry-like Series Modulo Primes

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