Cyclic sieving phenomenon
WebAbstract. We give a cyclic sieving phenomenon for symplectic -tableaux, SP( ;2m), where is a partition of an odd positive integer nand gcd(m;p) = 1 for any odd prime p n. We … 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
Cyclic sieving phenomenon
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WebCyclic Sieving? Victor Reiner, Dennis Stanton, and Dennis White Many finite sets in combinatorics have both cyclic symmetry and a natural generating function. Sur … 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 …
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 … 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 …
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 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 - an introduction, Korean lecture (pdf) , BCC lecture (pdf) . Descent and peak polynomials, pdf Discrete Morse Theory and generalized factor order, pdf Distance preserving graphs, pdf . Distance regular graphs and unimodality, dvi, ps, pdf . Factoring the characteristic polynomial, pdf .
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 … bombie 80k texture packWebThey carry not just W-actions, but W C-actions, where Cis the cyclic subgroup of Wgenerated by a Coxeter element. In the crystallographic case, both are isomorphic to the standard W- ... 3.1. First consequence: a cyclic sieving phenomenon 12 3.2. Second consequence: Kirkman and Narayana numbers for W 13 4. Proof of Proposition 2.10 14 … bomb id the forestWebOct 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 … gms monitoring centerWebA 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 … gms morgantownWebcations 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 ... gms mine services west virginiaWebcyclic sieving phenomenon. The straightforward equivalence between conditions (i) and(ii)aboveisproveninSection2,andrelatedtoalinear-algebraic/representation … bombiertes saphirglasWebSep 29, 2024 · Joshua Basman Monterrubio (Math and Theoretical Physical Sciences), Research in Pure Mathematics: Algebraic Combinatorics and the Cyclic Sieving Phenomenon, Dr. Anna Stokke. gms music peoria il