Related papers: The existence of a polynomial factorization map fo…

We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…

This is the first one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple linear groups.

We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly…

Two sets of conditions are presented for the compactness of a real plane algebraic curve, one sufficient and one necessary, in terms of the Newton polygon of the defining polynomial.

Raimi's theorem guarantees the existence of a partition of $\mathbb{N}$ into two parts with an unavoidable intersection property: for any finite coloring of $\mathbb{N}$, some color class intersects both parts infinitely many times, after…

This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…

This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

We show, for several fake projective planes with nontrivial automorphism group, that the bicanonical map is an embedding.

We show that the reduced point variety of a quantum polynomial algebra is the union of specific linear subspaces in $\mathbb{P}^n$, we describe its irreducible components and give a combinatorial description of the possible configurations…

We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible…

We investigate the uniqueness of factorisation of possibly disconnected finite graphs with respect to the Cartesian, the strong and the direct product. It is proved that if a graph has $n$ connected components, where $n$ is prime, or…

The N distinct prime numbers that make up a composite number M allow $2^{N-1}$ bi partioning into two relatively prime factors. Each such pair defines a pair of conjugate representations. These pairs of conjugate representations, each of…

Positive definite forms $f$ which are sums of squares are constructed to have the additional property that the members of any collection of forms whose squares sum to $f$ must share a nontrivial complex root.

We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference…

A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\Bbb R^2\to\Bbb R^2$ given by two polynomials of two variables. Such a transformation is called quadratic if the degrees of its polynomials are not greater than two. In…

The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to…

We determine a necessary and sufficient condition for a polynomial over an algebraically closed field $k$ to induce a surjective map on matrix algebras $M_n(k)$ for $n \ge 2$. The criterion is given in terms of critical points and uses…

Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field…

To a univariate monic polynomial is attached a special planar forest that is called the picture of the polynomial. Isotopy classes of pictures are called signatures. All combinatorially possible signatures are realized and spaces of…