A new dinv statistic on fall-decorated rectangular Dyck paths yields a proven q,t-generating function formula equal to the skewing operator applied to e_{m,n+km}, extending the rational shuffle theorem and the rise Delta theorem.
MR2371044 [Hai01] Mark Haiman, Hilbert schemes, polygraphs and the Macdonald positivity conjecture , J
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Falling stars: a fall-decorated rational shuffle theorem
A new dinv statistic on fall-decorated rectangular Dyck paths yields a proven q,t-generating function formula equal to the skewing operator applied to e_{m,n+km}, extending the rational shuffle theorem and the rise Delta theorem.