Related papers: Hultman elements for the hyperoctahedral groups

Lehmer's code defines a bijection between the symmetric group and the set of staircase compositions. In this paper, we characterize a poset structure on these compositions that is equivalent to the strong Bruhat order on the symmetric…

We study some properties and perspectives of the Hurwitz series ring $H_R[[t]]$, for a commutative ring with identity $R$. Specifically, we provide a closed form for the invertible elements by means of the complete ordinary Bell…

Kazhdan-Lusztig polynomials are important and mysterious objects in representation theory. Here we present a new formula for their computation for symmetric groups based on the Bruhat graph. Our approach suggests a solution to the…

In this paper we investigate some properties of ideals in group algebras of finite groups over fields. First, we highlight an important link between their dimension, their minimal Hamming distance and the group order. This is a generalized…

We borrow ideas from Grothendieck duality theory to noncommutative algebra, and use them to prove a reduction result for Hochschild cohomology for noncommutative algebras which are finite over their center. This generalizes a result over…

Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…

We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling…

In this paper we study pattern avoidance in Latin Squares, which gives us a two dimensional analogue of the well studied notion of pattern avoidance in permutations. Our main results include enumerating and characterizing the Latin Squares…

In connection with Vassiliev's knot invariants, Stoimenow introduced in 1998 a class of matchings, also known as regular linearized chord diagrams. These matchings are linked to various combinatorial structures, all of which are associated…

A normal variety $X$ is called $H$-spherical for the action of the complex reductive group $H$ if it contains a dense orbit of some Borel subgroup of $H$. We resolve a conjecture of Hodges--Yong by showing that their spherical permutations…

The theory of the column-row determinants has been considered for matrices over a non-split quaternion algebra. In this paper the concepts of column-row determinants are extending to a split quaternion algebra. New definitions of the column…

Let I_n(\pi) denote the number of involutions in the symmetric group S_n which avoid the permutation \pi. We say that two permutations \alpha,\beta\in\S{j} may be exchanged if for every n, k, and ordering \tau of j+1,...,k, we have…

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of…

The categories of real and of complex Hilbert spaces with bounded linear maps have received purely categorical characterisations by Chris Heunen and Andre Kornell. These characterisations are achieved through Sol\`er's theorem, a result…

For a Weyl group W and its reflection representation mathfrak{h}, we find the character and Hilbert series for a quotient ring of C[mathfrak{h} oplus mathfrak{h}^*] by an ideal containing the W--invariant polynomials without constant term.…

The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…

For all algebraic groups over non-Archimedean local fields, the bounded cohomology vanishes. This follows from the corresponding statement for automorphism groups of Bruhat--Tits buildings, which hinges on the solution to the flatmate…

We consider the ideal structure of Steinberg algebras over a commutative ring with identity. We focus on Hausdorff groupoids that are strongly effective in the sense that their reductions to closed subspaces of their unit spaces are all…

The purpose of this paper is to define cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were introduced by Makhlouf and Silvestrov in the study of one-parameter formal deformations…

Let $H$ be a permutation group on a set $\Lambda$, which is permutationally isomorphic to a finite alternating or symmetric group $A_n$ or $S_n$ acting on the $k$-element subsets of points from $\{1,\ldots,n\}$, for some arbitrary but fixed…