References & Citations
Mathematics > Combinatorics
Title: A conjectured formula for the rational $q,t$-Catalan polynomial
(Submitted on 1 Aug 2022 (v1), last revised 9 Feb 2023 (this version, v2))
Abstract: We conjecture a formula for the rational $q,t$-Catalan polynomial $\mathcal{C}_{r/s}$ that is symmetric in $q$ and $t$ by definition. The conjecture posits that $\mathcal{C}_{r/s}$ 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 $\{ \mathcal{C}_{r/s}^d: r\equiv 1 \mod s, \,\,\, d \leq d^*\}$ is equivalent to a finite counting problem.
Submission history
From: Graham Hawkes [view email][v1] Mon, 1 Aug 2022 02:28:35 GMT (33kb)
[v2] Thu, 9 Feb 2023 22:15:49 GMT (36kb)
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