Saúl A. Blanco
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Shortest path poset of finite Coxeter groups
dmtcs:2721 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2009,
DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
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https://doi.org/10.46298/dmtcs.2721
Shortest path poset of finite Coxeter groupsConference paper
Authors: Saúl A. Blanco 1
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Saúl A. Blanco
1 Department of Mathematics [Cornell]
We define a poset using the shortest paths in the Bruhat graph of a finite Coxeter group W from the identity to the longest word in W,w0. We show that this poset is the union of Boolean posets of rank absolute length of w0; that is, any shortest path labeled by reflections t1,…,tm is fully commutative. This allows us to give a combinatorial interpretation to the lowest-degree terms in the complete cd-index of W.