منابع مشابه
Bruhat interval polytopes
Let u and v be permutations on n letters, with u ≤ v in Bruhat order. A Bruhat interval polytope Qu,v is the convex hull of all permutation vectors z = (z(1), z(2), . . . , z(n)) with u ≤ z ≤ v. Note that when u = e and v = w0 are the shortest and longest elements of the symmetric group, Qe,w0 is the classical permutohedron. Bruhat interval polytopes were studied recently in the 2013 paper “The...
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An interval vector is a (0, 1)-vector where all the ones appear consecutively. Polytopes whose vertices are among these vectors have some astonishing properties that are highlighted in this paper. We present a number of interval-vector polytopes, including one class whose volumes are the Catalan numbers and another class whose face numbers mirror Pascal’s triangle.
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Recently EDELMAN & REINER suggested two poset structures S1(n;d) and S2(n;d) on the set of all triangulations of the cyclic dpolytope C(n;d) with n vertices. Both posets are generalizations of the well-studied Tamari lattice. While S2(n;d) is bounded by definition, the same is not obvious for S1(n;d). In the paper by EDELMAN & REINER the bounds of S2(n;d) were also confirmed for S1(n;d) wheneve...
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An interval vector is a (0, 1)-vector in Rn for which all the 1’s appear consecutively, and an interval-vector polytope is the convex hull of a set of interval vectors in Rn. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers ...
متن کاملOn the complete cd-index of a Bruhat interval
We study the non-negativity conjecture of the complete cd-index of a Bruhat interval as defined by Billera and Brenti. For each cd-monomial M we construct a set of paths, such that if a “flip condition” is satisfied, then the number of these paths is the coefficient of the monomial M in the complete cd-index. When the monomial contains at most one d, then the condition follows from Dyer’s proof...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.07.030