Related papers: New sequences of non-free rational points
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…
We give a description of elementary subgroups (in the sense of first-order logic) of finitely generated virtually free groups. In particular, we recover the fact that elementary subgroups of finitely generated free groups are free factors.…
Takahasi's theorem on chains of subgroups of bounded rank in a free group is generalized to several classes of semigroups. As an application, it is proved that the subsemigroups of periodic points are finitely generated and periodic orbits…
We consider noncommutative rational functions as well as matrices in polynomials in noncommuting variables in two settings: in an algebraic context the variables are formal variables, and their rational functions generate the "free field";…
In connection with Eisenstein series for the principal congruence subgroup $\Gamma(n)$, Hecke introduced certain numbers, of which he said that they are rational and cumbersome to calculate. We show, however, that these numbers are…
We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound…
We establish a new sufficient condition under which a monoid is non-finitely based and apply this condition to Lee monoids $L_\ell^1$, obtained by adjoining an identity element to the semigroup generated by two idempotents $a$ and $b$…
A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines $\displaystyle{{\left({}^{\alpha}{\mathbf B}_{i}^{k} \right)}_{i=0}^{k}}$ which depends on an index $\alpha…
The existence of an infinite simple boundedly generated 2-generated group and the existence of a boundedly simple 2-generated group containing a free non-cyclic subgroup are proved.
We consider a new class of non-Hermitian random matrices, namely the ones which have the form of sums of freely independent terms involving unitary matrices. To deal with them, we exploit the recently developed quaternion technique. After…
We show that the family of pseudo-random matrices recently discovered by Soloveychik, Xiang, and Tarokh in their work `Symmetric Pseudo-Random Matrices' exhibits asymptotic independence. More specifically, any two sequences of matrices of…
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
An elementary proof that certain pairs of $2\times 2$ matrices with nonnegative real coordinates generate free monoids.
We construct explicit non-isotrivial families of polynomials over $\mathbb{Q}$ satisfying uniform boundedness for their rational preperiodic points.
In this paper, we study algorithmic problems for automaton semigroups and automaton groups related to freeness and finiteness. In the course of this study, we also exhibit some connections between the algebraic structure of automaton…
A complex number $\lambda$ is said to be non-free if the subgroup of $SL(2,\bc)$ generated by $$X=\begin{pmatrix} 1& 1\\ 0 & 1 \end{pmatrix} \,\, \text{and}\,\,\,Y_{\lambda}=\begin{pmatrix} 1& 0\\ \lambda & 1 \end{pmatrix}$$ is not a free…
We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…
We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational…
We introduce the factorization graph of a finite group and study its connectedness and forbidden structures. We characterize all finite groups with connected factorization graphs and classify those with connected bipartite factorization…
The finite Pfaff lattice is given by commuting Lax pairs involving a finite matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The lattice admits solutions such that the entries of the matrix L are rational in the time…