4 research outputs found
Symmetry properties of the Novelli-Pak-Stoyanovskii algorithm
The number of standard Young tableaux of a fixed shape is famously given by
the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of
Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to
jeu-de-taquin which transforms an arbitrary filling of a partition into a
standard Young tableau by exchanging adjacent entries. Recently, Krattenthaler
and M\"uller defined the complexity of this algorithm as the average number of
performed exchanges, and Neumann and the author proved it fulfils some nice
symmetry properties. In this paper we recall and extend the previous results
and provide new bijective proofs.Comment: 13 pages, 3 figure, submitted to FPSAC 2014 Chicag