Bruhat Order of Coxeter Groups and Shellability
Anders Björner,Michelle L. Wachs +1 more
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This article is published in Advances in Mathematics.The article was published on 1982-01-01 and is currently open access. It has received 226 citations till now. The article focuses on the topics: Longest element of a Coxeter group & Coxeter complex.read more
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Shellable nonpure complexes and posets. II
Anders Björner,Michelle L. Wachs +1 more
TL;DR: In this paper, the applicability of lexicographic shellability to nonpure posets is discussed, and an edge-labeling λ of L(F) is defined as follows.
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On the Number of Reduced Decompositions of Elements of Coxeter Groups
TL;DR: Using the theory of symmetric functions, a formula is found for r(w) when W is the symmetric group Sn and for the element w0 ∈ Sn of longest length and certain other w ∉ Sn the formula is particularly simple.
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Gröbner geometry of Schubert polynomials
Allen Knutson,Ezra Miller +1 more
TL;DR: In this article, a determinantal ideal whose generators are certain minors in the generic n?~ n matrix (filled with independent variables) is considered, and the main theorems describe, for each ideal, the algebraic equivalence of the ideal.
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On lexicographically shellable posets
Anders Björner,Michelle L. Wachs +1 more
TL;DR: In this paper, a new recursive formulation of CL-shellability is introduced and exploited, and it is shown that face lattices of convex polytopes, totally semimodular posets, posets of injective and normal words, and lattice of bilinear forms are CLshellable.
References
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Book
Groupes et algèbres de Lie
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
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Hilbert functions of graded algebras
TL;DR: In this article, the additive group of R has a direct-sum decomposition R = R + R, +..., where RiRi C R,+j and 1 E R,.
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