Kento Nakada ; Shuji Okamura - An algorithm which generates linear extensions for a generalized Young diagram with uniform probability

dmtcs:2843 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2843
An algorithm which generates linear extensions for a generalized Young diagram with uniform probability

Authors: Kento Nakada 1; Shuji Okamura 2

  • 1 Wakkanai Hokusei Gakuen University
  • 2 Osaka Prefecture University

The purpose of this paper is to present an algorithm which generates linear extensions for a generalized Young diagram, in the sense of D. Peterson and R. A. Proctor, with uniform probability. This gives a proof of a D. Peterson's hook formula for the number of reduced decompositions of a given minuscule elements. \par

https://doi.org/10.46298/dmtcs.2843
Source: HAL:hal-01186271v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Generalized Young diagrams,Algorithm,linear extension,Kac-Moody Lie algebra,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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