Related papers: A generalized marriage theorem

The Schinzel hypothesis is a famous conjectural statement about primes in value sets of polynomials, which generalizes the Dirichlet theorem about primes in an arithmetic progression. We consider the situation that the ring of integers is…

We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences of the existence of Hall polynomials, in particular, we are…

We introduce a new type of mappings in metric space which are three-point analogue of the well-known Chatterjea type mappings, and call them generalized Chatterjea type mappings. It is shown that such mappings can be discontinuous as is the…

Let $k$ be an uncountable algebraically closed field of positive characteristic and let $S$ be a smooth projective connected surface over $k$. We extend the theorem on the Gysin kernel from [20, Theorem 5.1] to also be true over $k$, where…

In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…

We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials.

We generalize Gaeta's Theorem to the family of determinantal schemes. In other words, we show that the schemes defined by minors of a fixed size of a matrix with polynomial entries belong to the same G-biliaison class of a complete…

This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…

The following selection theorem is established:\\ Let $X$ be a compactum possessing a binary normal subbase $\mathcal S$ for its closed subsets. Then every set-valued $\mathcal S$-continuous map $\Phi\colon Z\to X$ with closed $\mathcal…

The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type…

Generalized distance-squared mappings are quadratic mappings of $\mathbb{R}^m$ into $\mathbb{R}^\ell$ of special type. In the case that matrices $A$ constructed by coefficients of generalized distance-squared mappings of $\mathbb{R}^2$ into…

In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…

We present here a more general version of the balanced pair algorithm. This version works in the reducible case and terminates more often than the standard algorithm. We present examples to illustrate this point. Lastly, we discuss the…

In this paper we are going to prove a very general fixed point theorem for mappings acting in partial metric spaces. In that theorem we impose some conditions on behavior of considered mappings on orbits and a condition relating orbits of…

We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are…

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…

This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…

A $biased\ graph$ is a pair $(G,\mathcal{B})$, where $G$ is a graph and $\mathcal{B}$ is a collection of `balanced' circuits of $G$ such that no $\Theta$-subgraph of $G$ contains precisely two balanced circuits. We prove a Ramsey-type…

In this paper, pursuing the same line of ideas in the proof of an old longstanding open conjecture of \emph{Kadison-Singer} , we introduce a key lemma which we call it the interlacing lemma which indicates a necessary condition for having a…

Consider an elliptic curve, defined over the rational numbers, and embedded in projective space. The rational points on the curve are viewed as integer vectors with coprime coordinates. What can be said about a rational point if a bound is…