منابع مشابه
Cyclic Sieving Phenomena on Annular Noncrossing Permutations
We show cyclic sieving phenomena on annular noncrossing permutations with given cycle types. We define annular q-Kreweras numbers, annular q-Narayana numbers, and annular q-Catalan numbers, and show that a sum of annular q-Kreweras numbers becomes an annular q-Narayana number and a sum of annular q-Narayana numbers becomes an annular q-Catalan number. We also show that these polynomials are clo...
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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.
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Abstract. Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially qanalogues, have useful interpretations related to actions and representations of the cyclic group. We define sieving for an arbitrary group G and study it for the dihedral group I2pnq of order 2n. This requires understanding the generators of the representation ring of the dihedral group. For ...
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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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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: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100803596