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

Ryan Kaliszewski, Debdut Karmakar


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.


Catalan; Dyck path; Parking function; Shuffle theorem; Rational shuffle theorem

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