Invariant Tensors and the Cyclic Sieving Phenomenon
نویسندگان
چکیده
منابع مشابه
Invariant Tensors and the Cyclic Sieving Phenomenon
We construct a large class of examples of the cyclic sieving phenomenon by exploiting the representation theory of semi-simple Lie algebras. Let M be a finite dimensional representation of a semi-simple Lie algebra and let B be the associated Kashiwara crystal. For r > 0, the triple (X, c, P ) which exhibits the cyclic sieving phenomenon is constructed as follows: the set X is the set of isolat...
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The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge’s q 1⁄4 1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Pólya–Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues. r 2004 Elsevier Inc. A...
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School of Mathematical and Statistical Sciences, Arizona State University Abstract. Reiner-Stanton-White defined the cyclic sieving phenomenon (CSP) associated to a finite cyclic group action on a finite set and a polynomial. Sagan observed the CSP on the set of non-crossing matchings on [2n] := {1, 2, . . . , 2n} using the cyclic group C2n generated by a cyclic shift of order 2n and the q-Cata...
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The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper. Let X be a finite set, C be a finite cyclic group acting on X , and f(q) be a polynomial in q with nonnegative integer coefficients. Then the triple (X,C, f(q)) exhibits the cyclic sieving phenomenon if, for all g ∈ C, we have #X = f(ω) where # denotes cardinality, X is the fixed point set of g, and ω is a ...
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A cyclic polytope of dimension d with n vertices is a convex polytope combinatorially equivalent to the convex hull of n distinct points on a moment curve in R. In this paper, we prove the cyclic sieving phenomenon, introduced by Reiner-StantonWhite, for faces of an even-dimensional cyclic polytope, under a group action that cyclically translates the vertices. For odd-dimensional cyclic polytop...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/4569