Corpus ID: 237504536

# An area-depth symmetric $q,t$-Catalan polynomial

@inproceedings{Pappe2021AnAS,
title={An area-depth symmetric \$q,t\$-Catalan polynomial},
author={Joseph Pappe and Digjoy Paul and Anne Schilling},
year={2021}
}
• Published 13 September 2021
• Mathematics
We define two symmetric q, t-Catalan polynomials in terms of the area and depth statistic and in terms of the dinv and dinv of depth statistics. We prove symmetry using an involution on plane trees. The same involution proves symmetry of the Tutte polynomials. We also provide a combinatorial proof of a remark by Garsia et al. regarding parking functions and the number of connected graphs on a fixed number of vertices.

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