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

Graham Hawkes

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalAnnals of Combinatorics
DOIs
StateAccepted/In press - 1 Jan 2023

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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