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
NULL##NULL
Kento Nakada;Shuji Okamura
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
GarcĂa-Segador, P.; Miranda, Pedro, 2018, Bottom-Up: A New Algorithm To Generate Random Linear Extensions Of A Poset, Order, 36, 3, pp. 437-462, 10.1007/s11083-018-9476-1.
Proctor, Robert A.; Scoppetta, Lindsey M., 2018, d-Complete Posets: Local Structural Axioms, Properties, And Equivalent Definitions, Order, 36, 3, pp. 399-422, 10.1007/s11083-018-9473-4.