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We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an…
Let $n$ be a positive integer, and let $k$ be a field (of arbitrary characteristic) accessible to symbolic computation. We describe an algorithmic test for determining whether or not a finitely presented $k$-algebra $R$ has infinitely many…
We calculate the minimal degree for a class of finite complex reflection groups $G(p,p,q)$, for $p$ and $q$ primes and establish relationships between minimal degrees when these groups are taken in a direct product.
We study a family of problems, called \prob{Maximum Solution}, where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean…
Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains…
Fields with only finitely many maximal subrings are completely determined. We show that such fields are certain absolutely algebraic fields and give some characterization of them. In particular, we show that the following conditions are…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
In this work, we reformulate the problem of existence of maximal elements for preference relations as a variational inequality problem in the sense of Stampacchia. Similarly, we establish the uniqueness of maximal elements using a…
In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M; (RFSG) residual finiteness of Schutzenberger groups of M; and (RFRL) residual finiteness of the natural actions of M on its…
Let G be a graph. Consider two nonadjacent vertices x and y that have a common neighbor. Folding G with respect to x and y is the operation which identifies x and y. After a maximal series of foldings the graph is a disjoint union of…
Building upon the previous Renner-Coxeter system of work by Eddy Godelle we introduce the familiar Renner monoid structure of the Adherence order. The Green's relations of the system are then considered in relation to the Adherence order…
In this paper, we introduce and investigate a new notion of exact sequences of semimodules over semirings relative to the canonical image factorization. Several homological results are proved using the new notion of exactness including some…
We determine upper and lower bounds for the number of maximum matchings (i.e., matchings of maximum cardinality) $m(T)$ of a tree $T$ of given order. While the trees that attain the lower bound are easily characterised, the trees with…
Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and…
We show that, for any cluster-tilted algebra of finite representation type over an algebraically closed field, the following three definitions of a maximal green sequence are equivalent: (1) the usual definition in terms of Fomin-Zelevinsky…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
We examine the degree structure $\mathbf{ER}$ of equivalence relations on $\omega$ under computable reducibility. We examine when pairs of degrees have a join. In particular, we show that sufficiently incomparable pairs of degrees do not…
We study maximal subsemigroups of the monoid T(X) of all full transformations on the set X=N of natural numbers containing a given subsemigroup W of T(X) where each element of a given set $U$ is a generator of T(X) modulo W. This note…
The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be…
Consider a measured equivalence relation acting on a bundle of hyperbolic metric spaces by isometries. We prove that every aperiodic hyperfinite subequivalence relation is contained in a {\em unique} maximal hyperfinite subequivalence…