Congruences for Catalan and Motzkin numbers and related sequences
By Emeric Deutsch, Bruce E. Sagan. 2004
97 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/6bc0d8f6466c38857627dcef8d3214c871a160d8
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Supercongruences for polynomial analogs of the Apéry numbers (2018, background): “Sagan [17] showed that, if λ ≥ 2 and μ ≥ 1, these sequences satisfy the supercongruences A(pn) ≡ A(n) (mod p(3)) (5) for all primes p ≥ 5 (in fact, a generalized version of these congruences already appears in M.”