A Linear Representation for Constant Term Sequences mod p^a with Applications to Uniform Recurrence

2025/03/27 by Kohen, Nadav
#11B50 (Primary) 68R15 #11B85 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.21988

Abstract

Many integer sequences including the Catalan numbers, Motzkin numbers, and the Apréy numbers can be expressed in the form ConstantTermOf[PⁿQ] for Laurent polynomials P and Q. These are often called ``constant term sequences''. In this paper, we characterize the prime powers, p^a, for which sequences of this form modulo p^a, and others built out of these sequences, are uniformly recurrent. For all other prime powers, we show that the frequency of 0 is 1. This is accomplished by introducing a novel linear representation of constant term sequences modulo p^a, which is of independent interest.

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