WebAug 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 …
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WebCyclic sieving De nition (Reiner{Stanton{White ’04) If Xis a nite set acted on by a cyclic group C n= hri, and X(q) is a polynomial in q, then the pair (X C n;X(q)) has the cyclic sieving phenomenon (CSP) if for all ‘2[n], #fx2X: r‘x= xg= X(!‘ n): Stier, Wellman, Xu Dihedral Sieving Phenomena July 25, 2024 5 / 29 WebWe show that whenever all parts of the integer partition λ are multiples of n, the underlying set of fillings exhibit the cyclic sieving phenomenon (CSP) under an n -fold cyclic shift of the columns. The corresponding CSP polynomial is given by E λ ( x; q; 0).
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 … WebCyclic Sieving Definition Given any set Cacted upon by the cyclic group Z n, a polynomial X(t) is a cyclic sieving polynomial for Cif ∀m,X(ζm n) = {w ∈C: cmw = w} , where ζ n is a primitive nth root of 1. Constants are cyclic sieving polynomials for repetition codes.
WebJul 1, 2014 · Suppose X is a finite set, C n = 〈 c 〉 a cyclic group acting on X, and f ∈ Z [q] a polynomial. The triple (X, C n, f) has the cyclic sieving phenomenon [19] if for all m, the number of elements of X fixed by c m is f (ζ m), where ζ is any primitive nth root of unity. D. White [27] discovered a cyclic sieving for 2 × n standard Young ... WebOct 1, 2024 · Introduction. The cyclic sieving phenomenon was introduced by Reiner–Stanton–White in [21]. Let X be a finite set on which a cyclic group C of order n …
WebIn many cases, the only known way to prove that a given @-analogue indeed is a cyclic sieving polynomial is to enumerate the number of fixed points of the group action and verify that the evaluation of the polynomial yields the same number. Remark 2. If (-,hdi, 5 (@))exhibits the cyclic sieving phenomenon, then so does d: , 5 (@)
WebMar 19, 2024 · As an application, we show a cyclic sieving phenomenon involving plane partitions under a sequence of piecewise-linear toggles. Subjects: Representation … godaddy service level agreementWebM. Bennett, B. Madill and A. Stokke, Jeu-de-taquin promotion and a cyclic sieving phenomenon for semistandard hook tableaux, Discrete Mathematics 319 (2014), 62-67. P. Campbell and A. Stokke, On the orthogonal tableaux of Koike and Terada, Annals of Combinatorics 17 (2013), 443-453. bonita springs vacation rentals beachfrontWebOct 1, 2024 · Then there exists an action of a cyclic group C of order n on SST m (λ) such that the triple (SST m (λ), C, q − κ (λ) s λ (1, q, q 2, …, q m − 1)) exhibits the cyclic sieving phenomenon. Remark 3.5. We do not know of an explicit cyclic group action yielding the cyclic sieving phenomenon predicted by Corollary 3.4 in general. bonita springs webcam liveWebThe 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 shown to appear in various situations, involving q-binomial coefficients, Pólya-Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some ... go daddy setting up dmarcWebApr 13, 2024 · In recent years, expanded polystyrene (EPS) lightweight soil has been widely used as subgrade in soft soil areas because of its light weight and environmental protection. This study aimed to investigate the dynamic characteristics of sodium silicate modified lime and fly ash treated EPS lightweight soil (SLS) under cyclic loading. The effects of EPS … godaddy setting up email forwardingWebThe cyclic sieving phenomenon V. Reiner,1 D. Stanton, and D. White Department of Mathematics, School of Mathematics, University of Minnesota, Minneapolis, MN 55455, … godaddy server not respondingWebApr 2, 2024 · Skew characters and cyclic sieving Per Alexandersson, Stephan Pfannerer, Martin Rubey, Joakim Uhlin In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. bonita springs tree lighting