Nonstandard analysis was born in the decade of 1960 an attempt to give a formal context to the Leibniz approach to differential calculus, in particular in order to provide a rigorous foundation to the notions of infinitesimal ...

Let L be a set of lines of an affine space over a field and let S be a set of points with the property that every line of L is incident with at least N points of S. Let D be the set of directions of the lines of L considered ...

Matroids are combinatorial objects that capture abstractly the essence of dependence. The Tutte polynomial, defined for matroids and graphs, has a numerous amount of information about these structures. In this thesis, we ...

We put forward a new algebraic framework to generalize and analyze Di e-Hellman like Decisional Assumptions which allows us to argue about security and applications by considering only algebraic properties. Our D`;k-MDDH ...

Let $\Gamma$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $\Gamma$ is an $r$-antipodal distance-regular graph if and only if the distance graph $\Gamma_d$ ...

Graph colouring is arguably one of the most important issues in Graph Theory. However, many of the questions that arise in the area such as the chromatic number problem or counting the number of proper colorings of a graph ...

This paper introduces a multiagent optimization algorithm inspired by the collective behavior of social insects. In our method, each agent encodes a possible solution of the problem to solve, and evolves in a way similar ...

A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ ...

We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, ...

En aquest treball es realitza un estudi de diferents conjunts i successions de notes musicals, com són les escales, els acords i les fileres de tons. Fent servir eines matemàtiques de la branca de la combinatòria es resolen ...