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Our main contribution here is the discovery of a new family of standard Youngtableaux $ {\cal T}^k_n$ which are in bijection with the family ${\calD}_{m,n}$ 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 sweepmap in the Fuss case by means of a very simple explicit algorithm. This newalgorithm has running time $O(m+n)$. It is independent of the Thomas-Williamalgorithm.

On the Sweep Map for Fuss Rational Dyck Paths