Related papers: Excedance number for involutions in complex reflec…

Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…

Much of the fascinating numerology surrounding finite reflection groups stems from Solomon's celebrated 1963 theorem describing invariant differential forms. Invariant differential derivations also exhibit interesting numerology over the…

In this article we give various formulates for compute the number of all coninvolutions over the group of upper triangular matrix with entries into the ring of Gaussian integers module $p$ and the ring of Quaternions integers module $p$,…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

We determine the Waring rank of the fundamental skew invariant of any complex reflection group whose highest degree is a regular number. This includes all irreducible real reflection groups.

The exact degree bound for the generators of rings of polynomial invariants is determined for the finite, non-cyclic groups having a cyclic subgroup of index two. It is proved that the Noether number of these groups equals one half the…

This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…

We prove a recent conjecture of Blanco and Petersen (arXiv:1206.0803v2) about an expansion formula for inversions and excedances in the symmetric group.

We call $i$ a fixed point of a given sequence if the value of that sequence at the $i$-th position coincides with $i$. Here, we enumerate fixed points in the class of restricted growth sequences. The counting process is conducted by…

In this paper, for a finite group, we discuss a method for calculating equivariant homology with constant coefficients. We apply it to completely calculate the geometric fixed points of the equivariant spectrum representing equivariant…

We introduce the notion of iterated group extensions, which, roughly speaking, is what one obtains by forming a group extension of a group extension. We interpret iterated extensions in terms of group cohomology, in the same way as…

Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…

The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we…

The differential cross-section for the reflection of light beams off rigid bodies obtained by the rotation of a generic derivable convex function is calculated. The calculation is developed using elementary notions of calculus and is…

It is shown that a finite group in which more than 3/4 of the elements are involutions must be an elementary abelian 2-group. A group in which exactly 3/4 of the elements are involutions is characterized as the direct product of the…

For a finite group generated by involutions, the involution width is defined to be the minimal $k\in\mathbb{N}$ such that any group element can be written as a product of at most $k$ involutions. We show that the involution width of every…

Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…

A Coxeter group W is called reflection independent if its reflections are uniquely determined by W only, independently on the choice of the generating set. We give a new sufficient condition for the reflection independence, and examine this…

We consider a stationary random field indexed by an increasing sequence of subsets of $\mathbb{Z}^d$ obeying a very broad geometrical assumption on how the sequence expands. Under certain mixing and local conditions, we show how the tail…

We derive a formula expressing the joint distribution of the cyclic valley number and excedance number statistics over a fixed conjugacy class of the symmetric group in terms of Eulerian polynomials. Our proof uses a slight extension of Sun…