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arXiv · 2110.06244

Congruence properties of combinatorial sequences via Walnut and the Rowland-Yassawi-Zeilberger automaton

Narad Rampersad·Jeffrey Shallit
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Abstract

Certain famous combinatorial sequences, such as the Catalan numbers and the Motzkin numbers, when taken modulo a prime power, can be computed by finite automata. Many theorems about such sequences can therefore be proved using Walnut, which is an implementation of a decision procedure for proving various properties of automatic sequences. In this paper we explore some results (old and new) that can be proved using this method.

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Narad Rampersad, Jeffrey Shallit. 2021-10-12. Congruence properties of combinatorial sequences via Walnut and the Rowland-Yassawi-Zeilberger automaton. https://arxiv.org/abs/2110.06244

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