Pure Mathematics Colloquium - Wholesale congruences for sequences arising in combinatorics

Dates

Wednesday, September 14, 2022 - 14:00 to 15:00

Speaker: Eric Rowland (Hofstra University)

Abstract: Over the last 15 years there have been a number of papers studying congruence properties of sequences, such as the Catalan numbers, that arise in combinatorial settings. Proofs of these properties have relied on methods particular to each sequence. However, by realizing a sequence as the diagonal of a rational power series in multiple variables, we can compute congruence information modulo prime powers in a completely automatic way. This approach reduces the proofs of many known results to routine computations, establishes new theorems for well-known sequences, and allows us to resolve some conjectures about the Apéry numbers. This is joint work with Reem Yassawi.