منابع مشابه
Shortest path poset of Bruhat intervals
Let [u, v] be a Bruhat interval and B(u, v) be its corresponding Bruhat graph. The combinatorial and topological structure of the longest u-v paths of B(u, v) has been extensively studied and is well-known. Nevertheless, not much is known of the remaining paths. Here we describe combinatorial properties of the shortest u-v paths of B(u, v). We also derive the non-negativity of some coefficients...
متن کاملShortest path poset of finite Coxeter groups
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 ...
متن کاملOn a Bruhat-like Poset
We investigate the combinatorics and the topology of the poset of strata of a Schubert like stratification on the Grassmannian of hermitian lagrangian spaces in Cn ⊕ Cn. We prove that this poset is a modular complemented lattice, we compute its Möbius function and we investigate the combinatorics and the topology of its order intervals.
متن کاملBruhat Intervals and Polyhedral Cones
Lecture notes by Matthew Dyer for lectures at the workshop “Coxeter groups and convex geometry.” 1. Root labelled Bruhat graph 1.1. Bruhat order. Let (W,S) be a Coxeter group. Bruhat order is the partial order defined by the following proposition; see [3] and [13] for more details. Proposition. There is a partial order ≤ on W with the following properties. Let w ∈ W and w = s1 . . . sn, n = l0(...
متن کاملInversion arrangements and Bruhat intervals
Let W be a finite Coxeter group. For a given w ∈ W , the following assertion may or may not be satisfied: (∗) The principal Bruhat order ideal of w contains as many elements as there are regions in the inversion hyperplane arrangement of w. We present a type independent combinatorial criterion which characterises the elements w ∈ W that satisfy (∗). A couple of immediate consequences are derive...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2012
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-012-0416-7