In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monoge...

The Appell-type polynomial family corresponding to the simplest non-commutative derivative operator turns out to be connected with the Boolean probability theory, the simplest of the three universal non-commutative probability theories (the other two being free and tensor/classical probability). The basic properties of the Boolean Appell polynomials are described. In particular, their generatin...

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan matrices to interpret some relationships between different families of polynomials. Moreover using the Hadamard product of series we get a general recurrence ...

Abstract Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A ′ n +1 ( x ) = + 1) with 0 constant polynomial. This allows us to obtain in simple way some known relations involving Apostol-Bernoulli polynomials, Apostol-Euler and generalized Bernoulli attached primitive Dirichlet character.

Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an involution that is also in the group of polynomial automorphisms. This form is a composition of a sequence of generalized Hénon maps together with two simple involu...

The graphical realization of a given degree sequence and partition adjacency matrix simultaneously is relevant problem in data driven modeling networks. Here we formulate common generalizations this the Exact Matching Problem, solve them with an algebraic Monte-Carlo algorithm that runs polynomial time if number classes bounded.

Let [Formula: see text] be a polynomial with the property that corresponding to every prime there exists an integer such text]. In this paper, we establish some equidistributed results between number of partitions whose parts are taken from sequence and those which in certain arithmetic progression.

The Independent Set problem is NP-hard in general, however polynomial time algorithms exist for the problem on various specific graph classes. Over the last couple of decades there has been a long sequence of papers exploring the boundary between the NPhard and polynomial time solvable cases. In particular the complexity of Independent Set on P5-free graphs has received significant attention, a...

let $d$ be a digraph with skew-adjacency matrix $s(d)$. then the skew energyof $d$ is defined to be the sum of the norms of all eigenvalues of $s(d)$. denote by$mathcal{o}_n$ the class of digraphs on order $n$ with no even cycles, and by$mathcal{o}_{n,m}$ the class of digraphs in $mathcal{o}_n$ with $m$ arcs.in this paper, we first give the minimal skew energy digraphs in$mathcal{o}_n$ and $mat...

For an odd integer n > 0, we introduce the class LPn of Laurent polynomials P (z) = (n+ 1) + n ∑ k=1 k odd ck(z k + z−k), with all coefficients ck equal to −1 or 1. Such polynomials arise in the study of Barker sequences of even length, i.e., integer sequences having minimal possible autocorrelations. We prove that polynomials P ∈ LPn have large Mahler measures, namely, M(P ) > (n + 1)/2. We co...