The rook monoid is lexicographically shellable
نویسندگان
چکیده
منابع مشابه
Planar Lattices are Lexicographically Shellable
The special properties of planar posets have been studied, particularly in the 1970's by I. Rival and others. More recently, the connection between posets, their corresponding polynomial rings and corresponding simplicial complexes has been studied by R. Stanley and others. This paper, using work of A. Bjorner, provides a connection between the two bodies of work, by characterizing when planar...
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Let n be a positive integer and let n = {1, . . . , n}. Let R be the set of all oneto-one maps σ with domain I (σ ) ⊆ n and range J (σ) ⊆ n. If i ∈ I (σ ) let iσ denote the image of i under σ . There is an associative product (σ, τ ) → στ on R defined by composition of maps: i(στ)= (iσ )τ if i ∈ I (σ ) and iσ ∈ I (τ ). Thus the domain I (στ) consists of all i ∈ I (σ ) such that iσ ∈ I (τ ). The...
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We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2019.05.009