Congruences for Catalan and Motzkin numbers and related sequences
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0407326,
title = {Congruences for Catalan and Motzkin numbers and related sequences},
author = {Emeric Deutsch and Bruce E. Sagan},
journal= {arXiv preprint arXiv:math/0407326},
year = {2007}
}
Comments
22 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan