On the Sweep Map for Fuss Rational Dyck Paths

2018/07/19 by Garsia, Adriano M., Xin, Guoce · 1 citation
#05A19 #05E40 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.07458

Abstract

Our main contribution here is the discovery of a new family of standard Young tableaux \cal T^k_n which are in bijection with the family \cal D_m,n of Rational Dyck paths for m=k× n± 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.

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• Symmetry of the refined q,t-Catalan polynomials for k-Dyck paths

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