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Cyclic sieving phenomenon

WebSimilar q -supercongruences are established for binomial coefficients and the Apéry numbers, by means of a general criterion involving higher derivatives at roots of unity. Our methods lead us to discover new examples of the cyclic sieving phenomenon, involving the q -Lucas numbers. Keywords: Gauss congruence supercongruence q -analogue We introduce analogues of the lattice of non-crossing set partitions for the … Dans un article paru en 1972, Germain Kreweras fit une étude des partitions … q-analogs of the Catalan numbers C n = (1 (n + 1))(n 2n) are studied from the view … Let B be a partially ordered product of three finite chains. For any group G of … The (type-A) associahedron is a polytope related to polygon dissections which … J. Fulman, P. M. Neumann, and, C. E. Praeger, A generating function … A simple bijection is given between dissections of a convex (n+2)-gon … We consider hooks, hook tableaux, rim hooks, and rim hook tableaux where all …

q$-dimensions of highest weight crystals and cyclic sieving phenomenon ...

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 at roots of unity; see Section... WebCyclic Sieving? Victor Reiner, Dennis Stanton, and Dennis White Many finite sets in combinatorics have both cyclic symmetry and a natural generating function. Sur … bob furniture discount outlet oxnard https://stealthmanagement.net

Cyclic sieving - Wikipedia

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. WebIn combinatorialmathematics, cyclic sievingis a phenomenon by which evaluating a generating functionfor a finite set at roots of unitycounts symmetry classes of objects … WebMar 5, 2024 · Hugh Thomas informed me that he and his collaborators were also thinking about cyclic sieving for minuscule P -partitions. I thank Jim Propp for informing me that he had independently and earlier (around 2016) conjectured the Type A … bob furniture dining sets

The cyclic sieving phenomenon

Category:Tableaux cyclic sieving - SymCat

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Cyclic sieving phenomenon

arXiv:1906.07420v1 [math.CO] 18 Jun 2024

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 … 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 = …

Cyclic sieving phenomenon

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WebB. E. Sagan , The cyclic sieving phenomenon: A survey, in Surveys in Combinatorics 2011, London Mathematical Society Lecture Note Series, Vol. 392 (Cambridge University … 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 ...

WebA 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 … WebAug 4, 2010 · Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially $q$-analogues, have useful interpretations related to actions …

WebOne of the most impressive instances of the cyclic sieving phenomenon is a theorem of Rhoades asserting that the set of plane partitions in a rectangular box under the action of promotion exhibits cyclic sieving. 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 …

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 associated to root systems are given by Fomin and Reading as a generalization of the cluster complexes found by Fomin and Zelevinsky. In this paper, the faces of various …

WebThe cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q=-1 phenomenon. The phenomenon is … bob furniture discount outlet locationsWebMar 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. The cyclic sieving polynomial is the -anologue of ... bob furniture discount outlet reclinerWebinstance 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. bob furniture discount outlet burbank ilWebAgain, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier result by B. Rhoades and later B. Fontaine and J. Kamnitzer. Finally, we consider certain skew ribbons, where promotion behaves in a predictable manner. This result is stated in form of a bicyclic sieving phenomenon. bob furniture discount outlet salem nhWebTHE CYCLIC SIEVING PHENOMENON V. REINER, D. STANTON, AND D. WHITE Abstract. The cyclic sieving phenomenon is de ned for generat-ing functions of a set a … bob furniture financeWebJan 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 … bob furniture freehold njWebJun 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 … bob furniture discount outlet tv stands