Séminaire Lotharingien de Combinatoire, 84B.24 (2020), 12 pp.

Eugene Gorsky, Mikhail Mazin and Monica Vazirani

Recursions for Rational q,t-Catalan Numbers

Abstract. We give a simple recursion labeled by binary sequences which computes rational q,t-Catalan power series, both in relatively prime and non relatively prime cases. It is inspired by, but not identical to recursions due to B. Elias, M. Hogancamp, and A. Mellit, obtained in their study of link homology. We also compare our recursion with that of Hogancamp-Mellit's and verify a connection between the Khovanov-Rozansky homology of (M,N) torus links and the rational q,t-Catalan power series for general positive M,N.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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