Congruences for Catalan and Motzkin numbers and related sequences

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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

Keywords

Combinatorics, 05A10 (Primary) 11A07 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/71941

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407326
 http://arxiv.org/abs/math/0407326

Collections

arXiv