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

We prove analogues for odd primes of results of Snaith and Barker-Snaith. Let l denote the p-complete connective Adams summand and consider the group of left l-module automorphisms of l smash l in the stable homotopy category which induce…

Let $Q$ be the matrix $\displaystyle \begin{pmatrix} a & b \\ 1 & 0 \end{pmatrix}$ in $GL_2(\mathbb{F}_q)$ where $\mathbb{F}_q$ is a finite field, and let $G$ be the finite cyclic group generated by $Q$. We consider the action of $G$ on the…

Questions concerning small fractional parts of polynomials and pseudo-polynomials have a long history in analytic number theory. In this paper, we improve on earlier work by Madritsch and Tichy. In particular, let $f=P+\phi$ where $P$ is a…

We introduce a new algebraic construction, {\em monop}, that combines monoids (with respect to the product of species), and operads (monoids with respect to the substitution of species) in the same algebraic structure. By the use of…

We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…

Let $\mathcal{V}_p(\lambda)$ be the collection of all functions $f$ defined in the unit disc $\ID$ having a simple pole at $z=p$ where $0<p<1$ and analytic in $\ID\setminus\{p\}$ with $f(0)=0=f'(0)-1$ and satisfying the differential…

Let $p$ be an idempotent ultrafilter over $\mathbb{N}$. For a positive integer $N$, let ${\cal P}_{\leq N}$ denote the additive group of polynomials $P\in\mathbb{Z}[x]$ with ${\rm deg}\, P\leq N$ and $P(0)=0$. Given a unitary operator $U$…

Given a partition $\lambda$, we write $e_j(\lambda)$ for the $j^{\textrm{th}}$ elementary symmetric polynomial $e_j$ evaluated at the parts of $\lambda$ and $e_jp_A(n)$ for the sum of $e_j(\lambda)$ as $\lambda$ ranges over the set of…

A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonality and triangularity relations. Although many…

Polynomial factoring has famous practical algorithms over fields-- finite, rational \& $p$-adic. However, modulo prime powers it gets hard as there is non-unique factorization and a combinatorial blowup ensues. For example, $x^2+p \bmod…

This is an English translation of Euler's ``Theoremata circa residua ex divisione potestatum relicta'', Novi Commentarii academiae scientiarum Petropolitanae 7 (1761), 49-82. E262 in the Enestrom index. Euler gives many elementary results…

The algebra of monodromy matrices for sl(n) trigonometric R-matrices is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product of L-operators.…

In this paper, we employ a version of Stepanov's method, developed by Hanson and Petridis, to prove several results on additive irreducibility of multiplicative subgroups in finite fields of prime order $p$. Specifically, we show that if a…

In this paper, we compute ${\rm Ext}_{A}^{s}(\widetilde{H}^*(B\mathbb{Z}/p),\mathbb{F}_p)$ for $s\leq 1$. Using this result, we investigate the behavior of $\varphi_3^{\mathbb{F}_p}$ and $\varphi_s^{\widetilde{H}^*(B\mathbb{Z}/p)}\…

The present paper deals with integral classes $\xi_p\in H_{2p+1}(L^{2p+1}\times L^{2p+1})$ which are counterexamples for the Steenrod realization problem, where $L^{2p+1}$ is the $(2p+1)$-dimensional lens space and $p\geq 3$ is a prime…

Let $p$ be an odd prime and $r\geq 1$. Suppose that $\alpha$ is a $p$-adic integer with $\alpha\equiv2a\pmod p$ for some $1\leq a<(p+r)/(2r+1)$. We confirm a conjecture of Sun and prove that…

This paper provides counterexamples to a previously conjectured upper bound on the first index $n_0$ at which a zero appears in constant term sequences of the form $A_p(n) = ct(P^n) \mod p$, where $P(t) \in \mathbb{Z}[t, t^{-1}]$. The…

The Steenrod squares are cohomology operations with important applications in algebraic topology. While these operations are well-understood classically, little is known about them in the setting of homotopy type theory. Although a…

We show that a family of multivariate polynomials recently introduced by Bessenrodt and Stanley can be expressed as solution of the octahedron recurrence with suitable initial data. This leads to generalizations and explicit expressions as…

We study automorphisms and representations of quasi polynomial algebras (QPAs) and quasi Laurent polynomial algebras (QLPAs). For any QLPA defined by an arbitrary skew symmetric integral matrix, we explicitly describe its automorphism…