Congruences for Catalan and Motzkin numbers and related sequences

Details Congruences for Catalan and Motzkin numbers and related sequences Congruences for Catalan and Motzkin numbers and related sequences

2004-07-19

arxiv.org/abs/math/0407326v1

Mathematics

Combinatorics

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

Scientific paper

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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