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- W2067681729 abstract "It is well known that a Coxeter group W , partially ordered by the Bruhat order, is a graded poset, with rank function given by the length, and that it is EL -shellable, hence Cohen–Macaulay, and Eulerian. We ask whether Invol ( W ) , the subposet of W induced by the set of involutions, is endowed with similar properties. If W is of type A or B , we proved, respectively in [F. Incitti, The Bruhat order on the involutions of the symmetric group, J. Algebraic Combin. 20 (2004), 243–261] and [F. Incitti, The Bruhat order on the involutions of the hyperoctahedral group, European J. Combin. 24 (2003), 825–848], that Invol ( W ) is graded, EL -shellable and Eulerian. In this work we complete the investigation on the classical Weyl groups, extending these results to type D and providing a unified description for the rank function." @default.
- W2067681729 created "2016-06-24" @default.
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- W2067681729 date "2006-07-01" @default.
- W2067681729 modified "2023-09-23" @default.
- W2067681729 title "Bruhat order on the involutions of classical Weyl groups" @default.
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- W2067681729 doi "https://doi.org/10.1016/j.aam.2005.11.002" @default.
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