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

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.