Cyclic sieving phenomenon

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August undefined, 2024

WebMar 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 ... WebT. 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.

The cyclic sieving phenomenon: A survey Request PDF

WebJan 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 … 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 … tailgate ramp system

Cyclic sieving phenomenon - Combinatorics - SageMath

Webcations 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 ... WebM. 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. … 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 … tailgate ramp for utility trailer

The cyclic sieving phenomenon — Experts@Minnesota

Skew characters and cyclic sieving - Cambridge

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 = … 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 … twilight alice and jasperWebMar 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 tailgater awd 500air filter

"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 … " - Cyclic sieving phenomenon

Cyclic sieving phenomenon

WebCyclic Sieving? Victor Reiner, Dennis Stanton, and Dennis White Many ﬁnite sets in combinatorics have both cyclic symmetry and a natural generating function. Sur … 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 be a …

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

WebAgain, 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. Webcluster complexes ∆(Φ). Thepurposeof this paperis to studythe cyclic sieving phenomenon for the faces of ∆s(Φ), along with a q-analogue X(q) of their face numbers, under a cyclic group action. Making use of Fomin and Reading’s results, we prove the cyclic sieving phenomenon by a combinatorial approach for ∆s(Φ) in type An, Bn, Dn ...

WebApr 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 … 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 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 …

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... tailgater airWebThe 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 … tailgate ramps for utility trailerWebinstance 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. tailgate ranch tonganoxie ksWebCyclic 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 tailgate range rover classicWebMar 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 … tailgate ranch walnut springsWebJun 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 … tailgate ranchWebIn combinatorialmathematics, cyclic sievingis a phenomenon by which evaluating a generating functionfor a finite set at roots of unitycounts symmetry classes of objects … tailgate ranch company