Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Douvropoulos, Theo"'
The cluster complex on one hand, parking functions on the other hand, are two combinatorial (po)sets that can be associated to a finite real reflection group. Cluster parking functions are obtained by taking an appropriate fiber product (over noncros
Externí odkaz:
http://arxiv.org/abs/2402.03052
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
The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. It has been a challenging open problem to determine which posets have real-rooted chain polynomials. Two new classes of posets, name
Externí odkaz:
http://arxiv.org/abs/2307.04839
Publikováno v:
SIGMA 19 (2023), 069, 40 pages
The generalized cluster complex was introduced by Fomin and Reading, as a natural extension of the Fomin-Zelevinsky cluster complex coming from finite type cluster algebras. In this work, to each face of this complex we associate a parabolic conjugac
Externí odkaz:
http://arxiv.org/abs/2209.12540
Autor:
Douvropoulos, Theo
In a finite Coxeter group $W$ and with two given conjugacy classes of parabolic subgroups $[X]$ and $[Y]$, we count those parabolic subgroups of $W$ in $[Y]$ that are full support, while simultaneously being simple extensions (i.e., extensions by a s
Externí odkaz:
http://arxiv.org/abs/2209.06201
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
Publikováno v:
Enum. Comb. Appl. 2:3 (2022) Article S2R20
The classical Hurwitz numbers count the fixed-length transitive transposition factorizations of a permutation, with a remarkable product formula for the case of minimum length (genus $0$). We study the analogue of these numbers for reflection groups
Externí odkaz:
http://arxiv.org/abs/2112.03427
Autor:
Chapuy, Guillaume, Douvropoulos, Theo
Publikováno v:
J. Algebra 602 (2022), 381--404
We give an elementary, case-free, Coxeter-theoretic derivation of the formula $h^nn!/|W|$ for the number of maximal chains in the noncrossing partition lattice $NC(W)$ of a real reflection group $W$. Our proof proceeds by comparing the Deligne-Readin
Externí odkaz:
http://arxiv.org/abs/2109.04341
Publikováno v:
In Journal of Algebra 1 March 2024 641:648-715