Related papers: On permutations induced by tame automorphisms over…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…
We find a formula for the number of permutation polynomials of degree q-2 over a finite field Fq, which has q elements, in terms of the permanent of a matrix. We write down an expression for the number of permutation polynomials of degree…
We prove that, in characteristic zero, closed subgroups of the polynomial automorphisms group containing the affine group contain the whole tame group.
It is known that automorphisms of finite-dimensional bound quiver algebras decompose into inner automorphisms and automorphisms which permute the vertices. In this paper, we show that for string algebras, automorphisms permuting vertices…
The goal of this paper is threefold. First, we describe the notion of dissociation for closed subgroups of the group of permutations on a countably infinite set and explain its numerous consequences on unitary representations…
We give a new proof of Fitzgerald's criterion for primitive polynomials over a finite field. Existing proofs essentially use the theory of linear recurrences over finite fields. Here, we give a much shorter and self-contained proof which…
We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.
In this paper, we present three classes of complete permutation monomials over finite fields of odd characteristic. Meanwhile, the compositional inverses of these complete permutation polynomials are also proposed.
We show how the sign of a permutation can be deduced from the tableaux induced by the permutation under the Robinson-Schensted-Knuth correspondence. The result yields a simple proof of a conjecture on the squares of imbalances raised by…
We prove an asymptotic formula for the number of permutation for which the associated permutation polynomial has degree smaller than $q-2$.
We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these…
The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.
The enumeration of points on (or off) the union of some linear or affine subspaces over a finite field is dealt with in combinatorics via the characteristic polynomial and in algebraic geometry via the zeta function. We discuss the basic…
In this paper, we consider the probability that a randomly chosen automorphism of a finite group fixes a randomly chosen element of a subgroup of that group. We obtain several new results as well as generalizations and improvements of some…
These are notes of my lectures at the summer school "Higher-dimensional geometry over finite fields" in Goettingen, June--July 2007. We present a proof of Tate's theorem on homomorphisms of abelian varieties over finite fields (including…
It is proved that the tame automorphism group of a differential polynomial algebra $k\{x,y\}$ over a field $k$ of characteristic $0$ in two variables $x,y$ with $m$ commuting derivations $\delta_1, \ldots, \delta_m$ is a free product with…
We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…