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.
Casagrande,The number of vertices of a Fano polytope, Annales de l’Institut Fourier56(2006), no
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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.