Sulzgruber, Robin - Symmetry properties of the Novelli-Pak-Stoyanovskii algorithm

dmtcs:2393 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Symmetry properties of the Novelli-Pak-Stoyanovskii algorithm

Authors: Sulzgruber, Robin

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 Müller 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.


Source : oai:HAL:hal-01207583v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: complexity,hook-length formula,Young tableaux,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]


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