A rational Catalan formula for \((m,3)\)-Hikita polynomials
Summary: Hikita polynomials are the combinatorial side of the rational shuffle theorem. Building upon a recent formula for \((m,3)\)-Catalan polynomials, we prove a formula for \((m,3)\)-Hikita polynomials in terms of 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 \((m,3)\)-Hikita polynomials.
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