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Description

In the $1980$ paper ``Une famille de Polynomes ayant Plusieurs Propriétés Enumeratives", Kreweras gives a bijection that shows that the polynomials $P_n(t)$ that enumerate $n$-labelled rooted trees by number of inversions also $t$-enumerates $n$-Parking Functions by the area statistic. In the $1993$ paper ``A Remarkable $q,t$-Catalan sequence and Lagrange Inversion" with Haiman we relate the Frobenius Characteristic of Diagonal Harmonics to Parking Functions. A recent search in the Encyclopedia of integer sequences connects these two papers in a surprising manner leading to a variety of beautiful conjectures. In this talk the focus will be on what we have proved.