Inverting the rational sweep map

    The Journal of Combinatorics, pp. 659-679, 2018.

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    Abstract:

    We announce a simple algorithm for inverting the sweep map on rational $(m,n)$-Dyck paths for a coprime pairs $(m,n)$ of positive integers. This work is inspired by Nathan Williams work on the modular sweep map. A direct and simple proof of the validity of our algorithm will appear in a forthcoming writing.

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