Related papers: Some monoids of Pisot matrices
We evaluate the number of monic polynomials (of arbitrary degree $N$) the zeros of which equal their coefficients when these are allowed to take arbitrary complex values. In the following, we call polynomials with this property {\em…
When doubly-affine matrices such as Latin and magic squares with a single non-zero eigenvalue are powered up they become constant matrices after a few steps. The process of compounding squares of orders m and n can then be used to generate…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
A subset $S$ of an integral domain $R$ is called a semidomain if the pairs $(S,+)$ and $(S, \cdot)$ are semigroups with identities; additionally, we say that $S$ is additively reduced provided that $S$ contains no additive inverses. Given…
A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we…
In this article we study the combinatorics of congruence subgroups of the modular group. We consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of Coxeter friezes),…
We show that for every subset $E$ of positive density in the set of integer square-matrices with zero traces, there exists an integer $k \geq 1$ such that the set of characteristic polynomials of matrices in $E-E$ contains the set of…
We study some of the factorization invariants of the class of Puiseux monoids generated by geometric sequences, and we compare and contrast them with the known results for numerical monoids generated by arithmetic sequences. The class we…
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…
We study the structure of the commutative multiplicative monoid $\mathbb N_0[x]^*$ of all the non-zero polynomials in $\mathbb Z[x]$ with non-negative coefficients. We show that $\mathbb N_0[x]^*$ is not a half-factorial monoid and is not a…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
We introduce several classes of monoids satisfying up to five axioms and establish basic theories on their arithmetics. The one satisfying all the axioms is named natural monoid. Two typical examples are 1) the monoid $\mathbb{N}$ of…
We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring arbitrary…
Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to…
We classify all matroids with at most 8 elements that have the half-plane property, and we provide a list of some matroids on 9 elements that have, and that do not have the half-plane property. Furthermore, we prove that several classes of…
We study monoids generated by various combinations of idempotents and one- or two-sided units of an infinite partial Brauer monoid. This yields a total of eight such monoids, each with a natural characterisation in terms of relationships…
A new property, the strong singular value property, is introduced, developed, and utilized to study the problem of which lists of nonnegative real numbers occur as the singular values of a matrix with a prescribed zero-nonzero pattern.
We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. This continues earlier work of Baeth, Cisto, et al.. On our…
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of…
We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…