Related papers: Linking first occurrence polynomials over F_p by S…

Let $F_2$ be the prime field of two elements and let $GL_s:= GL(s, F_2)$ be the general linear group of rank $s.$ Denote by $\mathscr A$ the Steenrod algebra over $F_2.$ The (mod-2) Lambda algebra, $\Lambda,$ is one of the tools to describe…

We study a particular class of infinite-dimensional representations of $\mathfrak{osp}(1|2n)$. These representations $L_n(p)$ are characterized by a positive integer $p$, and are the lowest component in the $p$-fold tensor product of the…

We prove an integrality property of the Chern character with values in Chow groups. As a consequence we obtain, for a prime number p, a construction of the p-1 first homological Steenrod operations on Chow groups modulo p and p-primary…

We consider a certain left action by the monoid $SL_2(\mathbf{N}_0)$ on the set of divisor pairs $\mathcal{D}_f := \{ (m, n) \in \mathbf{N}_0 \times \mathbf{N}_0 : m \lvert f(n) \}$ where $f \in \mathbf{Z}[x]$ is a polynomial with integer…

The purpose of this paper is to forge a direct link between the hit problem for the action of the Steenrod algebra A on the polynomial algebra P(n)=F_2[x_1,...,x_n], over the field F_2 of two elements, and semistandard Young tableaux as…

Let $p$ be a prime, let $d \geq 1$ be an integer and $A$ be the algebra of square matrices of size $d$ over the field of order $p$. Let $P, Q \in A[x_1, \dots x_n]$ be polynomials in $n$ indeterminates with coefficients in $A$, such that…

An alternative and combinatorial proof is given for a connection between a system of Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56…

Polynomial Lie (super)algebras $g_{pd}$ are introduced via $G_{i}$-invariant polynomial Jordan maps in quantum composite models with Hamiltonians $H$ having invariance groups $G_{i}$. Algebras $g_{pd}$ have polynomial structure functions in…

Attributed to J F Adams is the conjecture that, at odd primes, the mod-p cohomology ring of the classifying space of a connected compact Lie group is detected by its elementary abelian p-subgroups. In this note we rely on Toda's calculation…

We study some properties of the exponents of the terms appearing in the splitting perfect polynomials over $\mathbb{F}_{p^2}$, where $p$ is a prime number. This generalizes the work of Beard et al. over $\mathbb{F}_p$. Corrected paper.…

We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of $p$ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $N$…

This paper came to existence out of the desire to understand iterations of strictly triangular polynomial maps over finite fields. This resulted in two connected results: First, we give a generalization of $\F_p$-actions on $\F_p^n$ and…

We give a new construction of a weak form of Steenrod operations for Chow groups modulo a prime number p for a certain class of varieties. This class contains projective homogeneous varieties which are either split or over a field admitting…

We extend Wood's graph theoretic interpretation of certain quotients of the mod $2$ dual Steenrod algebra to quotients of the mod $p$ dual Steenrod algebra where $p$ is an odd prime and to quotients of the $C_2$-equivariant dual Steenrod…

We solve the first-order classification problem for rings $R$ of polynomials $F[x_1, \ldots,x_n]$ and Laurent polynomials $F[x_1,x_1^{-1}, \ldots,x_n,x_n^{-1}]$ with coefficients in an infinite field $F$ or the ring of integers $\mathbb Z$,…

We introduce explicit combinatorial interpretations for the coefficients in some of the transition matrices relating to skew Hall-Littlewood polynomials P_lambda/mu(x;t) and Hivert's quasisymmetric Hall-Littlewood polynomials G_gamma(x;t).…

The expression $a^n + b^n$ can be factored as $(a+b)(a^{n-1} - a^{n-2} b + a^{n-3} b^2 - ... + b^{n-1})$ when $n$ is an odd integer greater than one. This paper focuses on proving a few properties of the longer factor above, which we call…

Let $G$ be a simply connected and simple algebraic group defined and split over a finite prime field $\mathbb{F}_p$ of $p$ elements. In this paper, using an $\mathbb{F}_p$-linear map splitting Frobenius endomorphism on a hyperalgebra…

Recursive algebraic construction of two infinite families of polynomials in $n$ variables is proposed as a uniform method applicable to every semisimple Lie group of rank $n$. Its result recognizes Chebyshev polynomials of the first and…

For q > 2, Carlitz proved that the group of permutation polynomials (PPs) over F_q is generated by linear polynomials and x^{q-2}. Based on this result, this note points out a simple method for representing all PPs with full cycle over the…