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pro vyhledávání: '"Lewis, Joél"'
We show by an explicit example that the Garsia--Remmel $q$-rook numbers of Ferrers boards do not all have unimodal sequences of coefficients. This resolves in the negative a question from 1986 by the aforementioned authors.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2410.19714
Autor:
Lewis, Joel Brewster
We give analogues in the finite general linear group of two elementary results concerning long cycles and transpositions in the symmetric group: first, that the long cycles are precisely the elements whose minimum-length factorizations into transposi
Externí odkaz:
http://arxiv.org/abs/2407.20347
Previous work has shown that the disarray (or displacement) of an (affine) (signed) permutation is bounded in terms of its Coxeter length. Here, we characterize the permutations for which the bound is sharp in two ways: in terms of a natural property
Externí odkaz:
http://arxiv.org/abs/2404.06379
Autor:
Lewis, Joel Brewster, Wang, Jiayuan
In a finite real reflection group, the reflection length of each element is equal to the codimension of its fixed space, and the two coincident functions determine a partial order structure called the absolute order. In complex reflection groups, the
Externí odkaz:
http://arxiv.org/abs/2310.12265
We give uniform formulas for the number of full reflection factorizations of a parabolic quasi-Coxeter element in a Weyl group or complex reflection group, generalizing the formula for the genus-0 Hurwitz numbers. This paper is the culmination of a s
Externí odkaz:
http://arxiv.org/abs/2308.04751
Publikováno v:
Ann. Comb. (2023)
Petersen and Tenner defined the depth statistic for Coxeter group elements which, in the symmetric group, can be described in terms of a cost function on transpositions. We generalize that cost function to the other classical (finite and affine) Weyl
Externí odkaz:
http://arxiv.org/abs/2302.04404
Autor:
Lewis, Joel Brewster, Marberg, Eric
Publikováno v:
Forum of Mathematics, Sigma (2024), Vol. 12, Paper e22
The $K$-theoretic Schur $P$- and $Q$-functions $GP_\lambda$ and $GQ_\lambda$ may be concretely defined as weight generating functions for semistandard shifted set-valued tableaux. These symmetric functions are the shifted analogues of stable Grothend
Externí odkaz:
http://arxiv.org/abs/2209.03551
Publikováno v:
Hurwitz Orbits on Reflection Factorizations of Parabolic Quasi-Coxeter Elements. Electron. J. Combin. 31 (2024), no. 1, Paper 27
We prove that two reflection factorizations of a parabolic quasi-Coxeter element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the same subgroup and have the same multiset of conjugacy classes. As a lemma, we
Externí odkaz:
http://arxiv.org/abs/2209.00774
Publikováno v:
Journal of Algebra, vol. 641 (2024), pp. 648-715
We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections $\operatorname{Red}_W(g)$ of reduced r
Externí odkaz:
http://arxiv.org/abs/2209.00066
Autor:
Lewis, Joel Brewster, Rai, Mehr
Publikováno v:
Involve 17 (2024) 603-632
Consider a randomly shuffled deck of $2n$ cards with $n$ red cards and $n$ black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck that alternates in color by performing the following move: If the top
Externí odkaz:
http://arxiv.org/abs/2206.04614