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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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