For any permutation v, we show that the special matchings of v generate a Coxeter system. This gives new necessary conditions on an abstract poset to be isomorphic to a lower Bruhat interval of the symmetric group, and also answers in the affirmative, in the symmetric group case, a problem posed in [F. Brenti, F. Caselli, M. Marietti, Special matchings and Kazhdan–Lusztig polynomials, Adv. Math. 202 (2006) 555–601].
F. Caselli, F. Brenti, M. Marietti (2007). Special matchings and permutations in Bruhat orders. ADVANCES IN APPLIED MATHEMATICS, 38, 210-226 [10.1016/j.aam.2006.05.001].
Special matchings and permutations in Bruhat orders
CASELLI, FABRIZIO;
2007
Abstract
For any permutation v, we show that the special matchings of v generate a Coxeter system. This gives new necessary conditions on an abstract poset to be isomorphic to a lower Bruhat interval of the symmetric group, and also answers in the affirmative, in the symmetric group case, a problem posed in [F. Brenti, F. Caselli, M. Marietti, Special matchings and Kazhdan–Lusztig polynomials, Adv. Math. 202 (2006) 555–601].File in questo prodotto:
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