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arXiv · 1604.07456

Toric braids and $(m,n)$-parking functions

Anton Mellit
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Abstract

The Dyck path algebra construction of Carlsson and Mellit from arXiv:1508.06239 is interpreted as a representation of "the positive part" of the group of toric braids. Then certain sums over $(m,n)$-parking functions are related to evaluations of this representation on some special braids. The compositional $(km,kn)$-shuffle conjecture of Bergeron, Garsia, Leven and Xin from arXiv:1404.4616 is then shown to be a corollary of this relation.

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Anton Mellit. 2016-04-25. Toric braids and $(m,n)$-parking functions. https://doi.org/10.1215/00127094-2021-0011

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