Congruences for Catalan and Motzkin numbers and related sequences |
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| Authors: | Emeric Deutsch Bruce E. Sagan |
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| Affiliation: | a Department of Mathematics, Polytechnic University, Brooklyn, NY 11201, USA
b Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA |
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| 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 Cloitre and Zumkeller. The Thue-Morse sequence appears in several contexts. |
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