A Conjectured Formula for the Rational q, t -Catalan Polynomial

Graham Hawkes

doi:10.1007/s00026-023-00662-2

A Conjectured Formula for the Rational q, t -Catalan Polynomial

Graham Hawkes

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We conjecture a formula for the rational q, t-Catalan polynomial C_r_/_s that is symmetric in q and t by definition. The conjecture posits that C_r_/_s can be written in terms of symmetric monomial strings indexed by maximal Dyck paths. We show that for any finite d^∗ , giving a combinatorial proof of our conjecture on the infinite set of functions {Cr/sd:r≡1mods,d≤d∗} is equivalent to a finite counting problem.

Original language	English
Pages (from-to)	749-795
Number of pages	47
Journal	Annals of Combinatorics
Volume	28
Issue number	3
DOIs	https://doi.org/10.1007/s00026-023-00662-2
State	Accepted/In press - 1 Jan 2023

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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abstract = "We conjecture a formula for the rational q, t-Catalan polynomial Cr/s that is symmetric in q and t by definition. The conjecture posits that Cr/s can be written in terms of symmetric monomial strings indexed by maximal Dyck paths. We show that for any finite d∗ , giving a combinatorial proof of our conjecture on the infinite set of functions {Cr/sd:r≡1mods,d≤d∗} is equivalent to a finite counting problem.",

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A Conjectured Formula for the Rational q, t -Catalan Polynomial

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