The Johnson graph J(n, m) has the m-subsets of {1,2,…,n} as vertices and two subsets are adjacent in the graph if they share m-1 elements. Shapozenko asked about the isoperimetric function µn,m(k) of Johnson graphs, that ...

List k–Coloring (LI k-COL) is the decision problem asking if a given graph admits a proper coloring compatible with a given list assignment to its vertices with colors in {1,2,..., k}. The problem is known to be NP-hard ...

Given a subset D of the interval (0,1), if a Borel set A¿[0,1) contains no pair of elements whose difference modulo 1 is in D, then how large can the Lebesgue measure of A be? This is the analogue in the circle group of a ...

For k prime and A a finite set of integers with |A| ≥ $3(k-1)^2$ (k-1)! we prove that |A+k·A| ≥ (k+1)|A| − ⌈k(k+2)/4⌉ where k·A = {ka:a∈A}. We also describe the sets for which equality holds.

We prove a density version for the Ramsey statement that, for fixed r and sufficiently large n, every coloring of an abelian group of order n with r colors has nontrivial monochromatic solutions of the system Ax = 0, where ...

En aquest llibre s'ofereix una introducció a la probabilitat i a l'estadística adaptada a l'alumnat de primer curs d'una enginyeria tècnica, especialment les enginyeries relacionades amb les tecnologies de la informació. ...

We prove that, for all q=2 and for all invertible residue classes a modulo q, there exists a natural number n=(650q)9 that is congruent to a modulo q and that is the product of exactly three primes, all of which are below ...

In this article we present a punctured version of Alon's Nullstellensatz which states that if $f$ vanishes at nearly all, but not all, of the common zeros of some polynomials $g_1(X_1),\ldots,g_n(X_n)$ then every $I$-residue ...