Catálogo de publicaciones - libros

For non-trivial Heyting algebras , one always has at least one homomorphism →; if = there is at least one non-identical one. A Heyting algebra is if ∣ End()∣ = 2 and a system of almost rigid algebras ℌ is said to be if ∣ Hom(, )∣ = 1 for any two distinct , ∈ ℌ. We show that there exists a discrete system of 2 countable almost rigid Heyting algebras.

We use ergodic-theoretical tools to study various notions of “large” sets of integers which naturally arise in theory of almost periodic functions, combinatorial number theory, and dynamics. Call a subset of N a Bohr set if it corresponds to an open subset in the Bohr compactification, and a piecewise Bohr set (PWB) if it contains arbitrarily large intervals of a fixed Bohr set. For example, we link the notion of PWB-sets to sets of the form A+B, where A and B are sets of integers having positive upper Banach density and obtain the following sharpening of a recent result of Renling Jin.

Theorem. If A and B are sets of integers having positive upper Banach density, the sum set A+B is PWB-set.

We define an analogue of the the concept of J. H. Conway’s number games for games of multiple players. We define the value of such number game as an element of a vector space over the Conway field. We interpret the value in terms of the strategy of the game, and prove that all possible values in the vector space can occur.

Best possible estimates for the lengths of a Hamiltonian path and of a Hamiltonian polygon on a Euclidean simplex of given volume are given. The extreme cases are described.

A quasivariety ℚ is -universal if, for any quasivariety of algebraic systems of a finite similarity type, the lattice () of all subquasivarieties of is isomorphic to a quotient lattice of a sublattice of the lattice (ℚ) of all subquasivarieties of ℚ. We investigate -universality of finitely generated varieties of distributive double -algebras. In an earlier paper, we proved that any finitely generated variety of distributive double -algebras categorically universal modulo a group is also -universa1. Here we consider the remaining finitely generated varieties of distributive double -algebras and state a problem whose solution would complete the description of all -universal finitely generated varieties of distributive double -algebras.

The -triangle is a refined face count for the generalised cluster complex of Fomin and Reading. We compute the -triangle explicitly for all irreducible finite root systems. Furthermore, we use these results to partially prove the “ Conjecture” of Armstrong which predicts a surprising relation between the -triangle and the Möbius function of his -divisible partition poset associated to a finite root system.

For any coloring of the × grid using fewer than log log colors, one can always find a monochromatic equilateral right triangle, a triangle with vertex coordinates (), (), and ().

Assume that the edges of a complete bipartite graph are colored with colors. In this paper we study coverings of by vertex disjoint monochromatic cycles, connected matchings, and connected subgraphs. These problems occur in several applications.

The systems of linear equations (homogeneous or inhomogeneous) that are partition regular, over ℕ or ℤ or ℚ, were characterized by Rado. Our aim here is to characterize those systems for which we can guarantee a nonconstant, or injective, solution. It turns out that we thereby recover an equivalence between ℕ and ℤ that is normally lost when one passes from homogeneous to inhomogeneous systems.

The induced Ramsey number is the least positive integer such that there exists an N-vertex graph with the property that for each 2-coloring of its edges with red and blue, either some induced in subgraph isomorphic to has all its edges colored red, or some induced in subgraph isomorphic to has all its edges colored blue. In this paper, we study (, ) for various , where is the path with 3 vertices. In particular, we answer a question by Gorgol and Luczak by constructing a family { such that , where () is defined almost as , with the only difference that should be induced only of (not in itself) and should be induced only in the blue subgraph of .