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pro vyhledávání: '"Fishel, Susanna"'
The fundamental quasisymmetric functions in superspace are a generalization of the fundamental quasisymmetric functions involving anticommuting variables. We obtain the action of the product, coproduct, and antipode on the fundamental quasisymmetric
Externí odkaz:
http://arxiv.org/abs/2411.13371
Autor:
Dahlberg, Samantha, Fishel, Susanna
In this paper, we study the maximal chains of lattices which generalizes both the weak order and the Tamari lattice: certain lattices of maximal tubings. A maximal tubing poset $\mathfrak{L}(G)$ is defined for any graph $G$, but for the graphs we con
Externí odkaz:
http://arxiv.org/abs/2409.13898
Given an arbitrary Coxeter system $(W,S)$ and a nonnegative integer $m$, the $m$-Shi arrangement of $(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of $(W,S)$. The classical Shi arrangement ($m=0$) was introduced in the case of affi
Externí odkaz:
http://arxiv.org/abs/2303.16569
We give a non-negative combinatorial formula, in terms of Littlewood-Richardson numbers, for the homology of the unitary representations of the cyclotomic rational Cherednik algebra, and as a consequence, for the graded Betti numbers for the ideals o
Externí odkaz:
http://arxiv.org/abs/2008.04412
Autor:
Fishel, Susanna
Publikováno v:
In Recent trends in algebraic combinatorics, volume 16 of Assoc. Women Math. Ser., pages 75-113. Springer, Cham, 2019
In 1983, Lusztig defined a map $\sigma$ from affine permutations of $n$ to partitions of $n$. He conjectured that for any partition $\lambda$ of $n$, $\sigma^{-1}(\lambda)$ is a two-sided cell. Shi, in 1986, proved part of this conjecture. As a bypro
Externí odkaz:
http://arxiv.org/abs/1909.01257
Publikováno v:
J. Combin. Theory Ser. A 166 (2019), 144-170
We show that the ring of symmetric functions in superspace is a cocommutative and self-dual Hopf algebra. We provide formulas for the action of the coproduct and the antipode on various bases of that ring. We introduce the ring sQSym of quasisymmetri
Externí odkaz:
http://arxiv.org/abs/1907.09975
Publikováno v:
Discrete Applied Mathematics, 14-JAN-2019
Let ${\mathscr L}=(X,\preceq)$ be a lattice. For ${\cal P}\subseteq X$ we say that ${\cal P}$ is $t$-{\it intersecting} if ${\sf rank}(x\wedge y)\ge t$ for all $x,y\in{\cal P}$. The seminal theorem of Erd\H{o}s, Ko and Rado describes the maximum inte
Externí odkaz:
http://arxiv.org/abs/1904.01436
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Publikováno v:
European Journal of Combinatorics, Volume 74, December 2018, Pages 11-26
We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutation. We classify the permutations that achieve each of these bounds, and
Externí odkaz:
http://arxiv.org/abs/1708.04372
In this paper we present a bijection $\omega_n$ between two well known families of Catalan objects: the set of facets of the $m$-generalized cluster complex $\Delta^m(A_n)$ and the set of dominant regions in the $m$-Catalan arrangement ${\rm Cat}^m(A
Externí odkaz:
http://arxiv.org/abs/1302.2441