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We investigate a new class of Lie algebras, which are tame locally extended affine Lie algebras of nullity 1. It is an infinite-rank analog of affine Lie algebras, and their centerless cores are a local version of loop algebras. Such…

We present new theoretical results on the existence of intersective polynomials with certain prescribed Galois groups, namely the projective and affine linear groups $PGL_2(\ell)$ and $AGL_2(\ell)$ as well as the affine symplectic groups…

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

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…

Nearly complete intersection ideals were introduced by A. Boocher and J. Seiner (2018) and defines a special class of monomial ideals in a polynomial ring. These ideals were used to give a lower bound of the total sum of betti numbers that…

Recently, the investigation of Partially APN functions has attracted a lot of attention. In this paper, with the help of resultant elimination and MAGMA, we propose several new infinite classes of 0-APN power functions over…

Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their varied applications. For instance, in combinatorial design theory, a correspondence of perfect $c$-nonlinear…

We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…

Generalising the concept of a complete permutation polynomial over a finite field, we define completness to level $k$ for $k\ge1$ in fields of odd characteristic. We construct two families of polynomials that satisfy the condition of high…

We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…

In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius-Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of…

We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric polynomials.

We obtain function field analogues of recent energy bounds on modular square roots and modular inversions and apply them to bounding some bilinear sums and to some questions regarding smooth and square-free polynomials in residue classes.

We show that a profinite completion functor for (simplicial or topological) operads with good homotopical properties can be constructed as a left Quillen functor from an appropriate model category of infinity-operads to a certain model…

In this paper, a new construction of quaternary bent functions from quaternary quadratic forms over Galois rings of characteristic 4 is proposed. Based on this construction, several new classes of quaternary bent functions are obtained, and…

In this paper we consider in detail the composition of an irreducible polynomial with X^2 and suggest a recurrent construction of irreducible polynomials of fixed degree over finite fields of odd characteristics. More precisely, given an…

The class B of lacunary polynomials f(x) := -1 + x + x^n + x^{m_1} + x^{m_2} + ... + x^{m_s}, where s >= 0, m_1 - n >= n - 1, m_{q+1} - m_{q} >= n - 1 for 1 <= q < s, n >= 3 is studied. A polynomial having its coefficients in {0, 1} except…

In the first part we study nearly Frobenius algebras. The concept of nearly Frobenius algebras is a generalization of the concept of Frobenius algebras. Nearly Frobenius algebras do not have traces, nor they are self-dual. We prove that the…

Regarding non-unique factorization of integer-valued polynomials over a discrete valuation domain $(R,M)$ with finite residue field, it is known that there exist absolutely irreducible elements, that is, irreducible elements all of whose…

It is well-known that a polynomial f(z)=a_d z^d(1+o(1)) can be conjugated by a holomorphic map phi to w \mapsto w^d in a neighbourhood of infinity. This map phi is called a B\"ottcher coordinate for f near infinity. In this paper we…