منابع مشابه
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 ...
متن کاملPromotion and Cyclic Sieving via Webs
We show that Schützenberger’s promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this action admits the cyclic sieving phenomenon.
متن کاملCyclic 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...
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2010
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.03.017