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An algorithm which generates linear extensions for a generalized Young diagram with uniform probability
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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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 
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     author = {Nakada, Kento and Okamura, Shuji},
     title = {An algorithm which generates linear extensions for a generalized {Young} diagram with uniform probability},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2843},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2843/}
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Nakada, Kento; Okamura, Shuji. An algorithm which generates linear extensions for a generalized Young diagram with uniform probability. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2843. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2843/

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