On the Sweep Map for Fuss Rational Dyck Paths

Abstract

Our main contribution here is the discovery of a new family of standard Young tableaux ${\mathcal{T}}_n^k$ which are in bijection with the family ${\mathcal{D}}_{m,n}$ of Rational Dyck paths for $m=k\times n\pm 1$ (the so called "Fuss" case). Using this family we give a new proof of the invertibility of the sweep map in the Fuss case by means of a very simple explicit algorithm. This new algorithm has running time $O(m+n)$. It is independent of the Thomas-William algorithm.

24 pages, 7 figures

Cited by in corpus (1)

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