A multi-vertex modification of the Kostant game bijects with minimal length coset representatives in Weyl group quotients W/W_J, yielding algorithmic views on reduced words plus new identities and foundations for the Mukai conjecture.
Winkel,A combinatorial bijection between standard Young tableaux and reduced words of Grassmannian permutations, Séminaire Lotharingien de Combinatoire36(1996), Article B36h
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Weyl Groups and the Modified Kostant Game
A multi-vertex modification of the Kostant game bijects with minimal length coset representatives in Weyl group quotients W/W_J, yielding algorithmic views on reduced words plus new identities and foundations for the Mukai conjecture.