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Congruences for Catalan and Motzkin numbers and related sequences

✍ Scribed by Emeric Deutsch; Bruce E. Sagan

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 238 KB
Volume: 117
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2005.06.005

No coin nor oath required. For personal study only.

✦ Synopsis

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 Cloitre and Zumkeller. The Thue-Morse sequence appears in several contexts.

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