The cyclic sieving phenomenon
Webcyclic sieving phenomenon. The straightforward equivalence between conditions (i) and(ii)aboveisproveninSection2,andrelatedtoalinear-algebraic/representation … WebThe 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. Keywords Hook formula Kraskiewicz-Weyman Noncrossing partitions Ordered tree Polygon dissections Principal specialization
The cyclic sieving phenomenon
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WebNov 18, 2024 · We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level ℓ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way not depending on types, ranks and levels. In order to do that, we introduce S-evaluation on the set of … WebJan 23, 2024 · Abstract. In this note, we provide a short proof of Theorem 4.3 in the paper titled Crystals, semistandard tableaux and cyclic sieving phenomenon, by Y.-T. Oh and E. …
WebThe cyclic sieving phenomenon - an introduction Bruce Sagan Department of Mathematics Michigan State University East Lansing, MI 48824-1027 [email protected] WebAug 7, 2024 · The Cone of Cyclic Sieving Phenomena Article Full-text available Apr 2024 DISCRETE MATH Per Alexandersson Nima Amini View Show abstract Canonical bases for the quantum group of type $A_r$ and...
WebThe triple (S;G;f(q)) exhibits the cyclic sieving phenomenon (c.s.p.) if, for all g 2G, we have #Sg = f(!): where !is chosen so that o(!) = o(g). Notes. 1. At first blush, this is a surprising equation. 2. The case #G = 2 was first studied by Stembridge. 3. Dozens of c.s.p.’s have been found. 4. Three proof techniques: evaluation ... WebThe 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 …
WebJun 19, 2024 · exhibits the cyclic sieving phenomenon, where C is the cyclic group generated by c (see Theorem 3.3). There are several examples for which our cyclic sieving phenomenon hold without the condition gcd(n, λ ) = 1, and Remark 3.4 shows an example for another cyclic sieving phenomenon with a specialization of sλ other than the principal ...
WebMay 21, 2024 · Skew characters and cyclic sieving - Volume 9. In 2010, Rhoades proved that promotion on rectangular standard Young tableaux, together with the associated fake-degree polynomial, provides an instance of the cyclic sieving phenomenon. look up a realtor licenseWebThe cyclic sieving phenomenon has been studied extensively since its introduc-tion in 2004 [RSW04]. Briefly, this phenomenon relates a cyclic group action on a set of combinatorial objects with a q-analog of the cardinality of the set evaluated at roots of unity. 1.1. Cyclic sieving The notion of cyclic sieving is defined as follows ... horace andy fools fall in loveWebJan 9, 2024 · The cyclic sieving phenomenon See below for the definition of the cyclic sieving phenomenon, (CSP). There are many instances of the CSP, which I have put into … horace andy albumsWebMar 16, 2024 · We give a cyclic sieving phenomenon for symplectic -tableaux, , where is a partition of an odd positive integer and for any odd prime . We use the crystal structure on Kashiwara-Nakashima symplectic tableaux to get a cyclic sieving action as the product of simple reflections in the Weyl group. look up area codes freeWebT. Pressey, A. Stokke and T. Visentin, Increasing tableaux, Narayana numbers and an instance of the cyclic sieving phenomenon, Annals of Combinatorics, Ann. Comb. 20 (2016), 609-621. A. Stokke, Global crystal bases and q-Schur algebras, Journal of Algebra and its Applications 14 (8) (Oct. 2015), 1-21. horace andy et massive attackWebIn this paper we study the Hecke algebra associated with a complex reflection group W. We discuss some properties of the Galois group of the splitting field of this algebra, and study its action on the so-called fake degrees of W. The methods we use to study the Hecke algebra are based on the construction of representations of this algebra as monodromy … horace andy collie herbWebOct 1, 2024 · From the viewpoint of the cyclic sieving phenomenon, the above computation modulo q n − 1 says that there exists an action of a cyclic group C of order n on B (Λ), … lookup area codes for free