Cyclic Sieving and Rational Catalan Theory

نویسندگان
چکیده

منابع مشابه

Cyclic Sieving and Rational Catalan Theory

Let a < b be coprime positive integers. Armstrong, Rhoades, and Williams (2013) defined a set NC(a, b) of ‘rational noncrossing partitions’, which form a subset of the ordinary noncrossing partitions of {1, 2, . . . , b− 1}. Confirming a conjecture of Armstrong et. al., we prove that NC(a, b) is closed under rotation and prove an instance of the cyclic sieving phenomenon for this rotational act...

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Cyclic sieving, promotion, and representation theory

We prove a collection of conjectures of D. White [37], as well as some related conjectures of Abuzzahab-Korson-Li-Meyer [1] and of Reiner and White [21], [37], regarding the cyclic sieving phenomenon of Reiner, Stanton, and White [22] as it applies to jeu-de-taquin promotion on rectangular tableaux. To do this, we use Kazhdan-Lusztig theory and a characterization of the dual canonical basis of ...

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Cyclic 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.

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The 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...

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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...

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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2016

ISSN: 1077-8926

DOI: 10.37236/5681