Cyclic sieving phenomenon
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 ... Webthat exhibits cyclic sieving and a class of subsets of the ASM(n) that exhibit cyclic sieving with gyration and a new set of polynomials. Contents 1. Introduction 1 2. Cyclic Sieving Phenomenon with Rotation 4 3. Cyclic Sieving Phenomenon with Gyration 6 4. The Generalized Symmetric Group 9 5. A Set of ASMs on which Gyration is Well-Behaved 12 6.
Cyclic sieving phenomenon
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Webinstance of the cyclic sieving phenomenon [RSW04] previously established through more di cult tools in [Rho10]. While de nitions have been proposed for slrwebs with r 3 [Kim03, Mor07, Wes12, Fon12], the resulting constructions are not entirely satisfactory from our perspective, as they lack important combinatorial properties. WebOct 1, 2004 · The cyclic sieving phenomenon (CSP ) of Reiner-Stanton-White [12] encodes the orbit structure of a cyclic action on a finite set in evaluations of a polynomial …
WebImplementation of the Cyclic Sieving Phenomenon as described by Reiner, Stanton, and White in [RSW2004]. We define the CyclicSievingPolynomial () of a finite set S together … WebOct 1, 2024 · In this paper, we compute explicitly the q - dimensions of highest weight crystals modulo q n − 1 for a quantum group of arbitrary finite type under certain assumptions, and interpret the modulo computations in terms of the cyclic sieving phenomenon. Let g be a finite-dimensional simple Lie algebra over ℂ and U q ( g) be its …
WebThe cyclic sieving phenomenon owes its name to the fact that, mysteriously often, the most natural @-analogue of the counting formula for the cardinality of - as a function of = is a cyclic sieving polynomial. In many cases, the only known way to prove that a given @-analogue indeed is a cyclic WebOct 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 …
WebAug 7, 2024 · In this paper, we compute explicitly the $q$-dimensions of highest weight crystals modulo $q^n-1$ for a quantum group of arbitrary finite type under certain assumption, and interpret the modulo... lakai riley 2WebMar 16, 2024 · 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. Park, which concerns a cyclic sieving … Expand lakai restaurant salt lake cityWebOct 1, 2004 · The cyclic sieving phenomenon (CSP ) of Reiner-Stanton-White [12] encodes the orbit structure of a cyclic action on a finite set in evaluations of a polynomial at roots of unity; see Section... lakair lodge monetville ontarioWebcations of this theory to cyclic sieving phenomena involving reduced words for the long elements of hyperoctohedral groups, handshake patterns, and noncrossing partitions. Keywords: Kazhdan-Lusztig theory, combinatorial actions, tableaux 1 Introduction Let X be a finite set, C = hci be a cyclic group acting on X, and X(q) be a polynomial in Z ... lakai running shoesWebCyclic Sieving? Victor Reiner, Dennis Stanton, and Dennis White Many finite sets in combinatorics have both cyclic symmetry and a natural generating function. Sur … lakai riley 3 shoesWebA list of instances of the cyclic sieving phenomenon on tableaux and fillings The symmetric functions catalog An overview of symmetric functions and related topics IndexCSPTopicsMeta Standard Young tableaux Rectangular SYT Stretched SYT Staircase and other SYT Semistandard type tableaux Rectangular SSYT Hook SSYT SSYT of … la kai restaurantWebAug 4, 2010 · The cyclic sieving phenomenon: a survey. Bruce E. Sagan. The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper. Let X be a … la kai salt lake city