A Rational Catalan Formula for $(m,3)$-Hikita Polynomials

TL;DR

This paper presents a new formula for $(3,m)$-Hikita polynomials that reveals their recursive structure and proves their $q,t$-symmetry, extending recent work on related Catalan polynomials.

Contribution

It introduces a rational Catalan formula for $(3,m)$-Hikita polynomials, connecting them to Catalan polynomials and uncovering their recursive and symmetric properties.

Findings

Established a formula relating $(3,m)$-Hikita and Catalan polynomials

Proved the $q,t$-symmetry of $(3,m)$-Hikita polynomials

Revealed recursive relations among coefficients

Abstract

Building upon a recent formula for $(3,m)$-Catalan polynomials, we describe a formula for $(3,m)$-Hikita polynomials in terms related to Catalan polynomials. This formula shows a surprising relation among coefficients of Hikita polynomials and implies deeper recursive relations and proves the $q,t$-symmetry of $(3,m)$-Hikita polynomials.