Generalized Coinvariant Algebras for $G(r,1,n)$ in the Stanley-Reisner setting
نویسندگان
چکیده
منابع مشابه
Colimits, Stanley-Reisner Algebras, and Loop Spaces
We study diagrams associated with a finite simplicial complex K, in various algebraic and topological categories. We relate their colimits to familiar structures in algebra, combinatorics, geometry and topology. These include: right-angled Artin and Coxeter groups (and their complex analogues, which we call circulation groups); Stanley-Reisner algebras and coalgebras; Davis and Januszkiewicz’s ...
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We give a purely combinatorial characterization of complete Stanley-Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.
متن کاملTail Positive Words and Generalized Coinvariant Algebras
Let n, k, and r be nonnegative integers and let Sn be the symmetric group. We introduce a quotient Rn,k,r of the polynomial ring Q[x1, . . . , xn] in n variables which carries the structure of a graded Sn-module. When r > n or k = 0 the quotient Rn,k,r reduces to the classical coinvariant algebra Rn attached to the symmetric group. Just as algebraic properties of Rn are controlled by combinator...
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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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We survey the Stanley-Reisner correspondence in combinatorial commutative algebra, describing fundamental applications involving Alexander duality, associated primes, f and h-vectors, and Betti numbers of monomial ideals.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8109