منابع مشابه
Cyclic Sieving and Cluster Multicomplexes
Reiner, Stanton, and White [10] proved results regarding the enumeration of polygon dissections up to rotational symmetry. Eu and Fu [2] generalized these results to Cartan-Killing types other than A by means of actions of deformed Coxeter elements on cluster complexes of Fomin and Zelevinsky [6]. The ReinerStanton-White and Eu-Fu results were proven using direct counting arguments. We give rep...
متن کاملThe Cyclic Sieving Phenomenon for Faces of Generalized Cluster Complexes
The notion of cyclic sieving phenomenon is introduced by Reiner, Stanton, and White as a generalization of Stembridge’s q = −1 phenomenon. The generalized cluster complexes associated to root systems are given by Fomin and Reading as a generalization of the cluster complexes found by Fomin and Zelevinsky. In this paper, the faces of various dimensions of the generalized cluster complexes in typ...
متن کاملCyclic Sieving for Cyclic Codes
These are notes on a preliminary follow-up to a question of Jim Propp, about cyclic sieving of cyclic codes. We show that two of the Mahonian polynomials are cyclic sieving polynomials for certain Dual Hamming Codes: X and X inv for q = 2, 3 and q = 2, respectively.
متن کاملThe cyclic sieving phenomenon
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...
متن کاملCyclic Sieving of Matchings
Let Pn denote the poset of matchings on 2n points on a circle, labeled 1, 2, . . . , 2n in cyclic order, in which we define an element to be less than another element if it can be obtained by an uncrossing. Let Pn,k denote the level of the poset with k crossings. Let Pn,k denote the level of the poset with k crossings. We study the cyclic sieving phenomenon of Pn,k. It is known that the triple ...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2010
ISSN: 0196-8858
DOI: 10.1016/j.aam.2010.03.003