Related papers: Elementary divisors of Cartan matrices for symmetr…

The object of this paper is to examine finite solvable groups whose integral group rings have only trivial central units.

In this paper we investigate a spectra of the Laplacian matrix of cyclic groups using the properties of their characteristic polynomials. We have proved several assertions about the relationship between the spectra of different groups.

We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding an elementary proof. Our result is…

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.

We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…

The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…

We comment two papers of Domokos and Vaccarino proving that the restriction to diagonal matrices of the scheme of commuting matrices is an isomorphism when restricted to invariants to the symmetric group invariants.

The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…

In this work, we give a new method to compute the Hilbert basis of the semigroup of certain positive divisors supported on the exceptional divisor of a normal surface singularity. Our approach is purely combinatorial which permits to avoid…

This is an introduction to the group algebras of the symmetric groups, written for a quarter-long graduate course. After recalling the definition of group algebras (and monoid algebras) in general, as well as basic properties of…

Let $\p_N \colon \tX \to X$ be a regular covering projection of connected graphs with the group of covering transformations isomorphic to $N$. If $N$ is an elementary abelian $p$-group, then the projection $\p_N$ is called $p$-elementary…

In this paper we evaluate Chebyshev polynomials of the second-kind on a class of symmetric integer matrices, namely on adjacency matrices of simply laced Dynkin and extended Dynkin diagrams. As an application of these results we explicitly…

We prove a categorification of the stable elements formula of Cartan and Eilenberg. Our formula expresses the derived category and the stable module category of a group as a bilimit of the corresponding categories for the $p$-subgroups.

There is a simple formula for the Ehrhart polynomial of a cyclic polytope. The purpose of this paper is to show that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any…

We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…

We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.

A compound determinant identity for minors of rectangular matrices is established. As an application, we derive Vandermonde type determinant formulae for classical group characters.

The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from…

We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…

This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.