Emeric Deutsch, Bruce E. Sagan
Published 2004-07-19Version 1
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.
Comments: 22 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan
A congruence involving products of $q$-binomial coefficients
On Motzkin numbers and central trinomial coefficients
On the divisibility of $q$-trinomial coefficients
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