0-Hecke Algebra Action on the Stanley-Reisner Ring of the Boolean Algebra
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چکیده
منابع مشابه
0-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra
We define an action of the 0-Hecke algebra of type A on the Stanley-Reisner ring of the Boolean algebra. By studying this action we obtain a family of multivariate noncommutative symmetric functions, which specialize to the noncommutative Hall-Littlewood symmetric functions and their (q, t)-analogues introduced by Bergeron and Zabrocki. We also obtain multivariate quasisymmetric function identi...
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In [2], Billera proved that the R-algebra of continuous piecewise polynomial functions (C0 splines) on a d-dimensional simplicial complex 1 embedded in Rd is a quotient of the Stanley–Reisner ring A1 of 1. We derive a criterion to determine which elements of the Stanley–Reisner ring correspond to splines of higher-order smoothness. In [5], Lau and Stiller point out that the dimension of C k (1)...
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Let (W, I) be a finite Coxeter group. In the case where W is a Weyl group, Berenstein and Kazhdan in [BK] constructed a monoid structure on the set of all subsets of I using unipotent χ-linear bicrystals. In this paper, we will generalize this result to all types of finite Coxeter groups (including non-crystallographic types). Our approach is more elementary, based on some combinatorics of Coxe...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2015
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-015-0264-y