This paper considers the multi-period service scheduling problem with an aperiodic service policy. In this problem, a set of customers who periodically require service over a finite time horizon is given. To satisfy the ...

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 ...

The problem of district design for the implementation of arc routing activities is addressed. The aim is to partition a road network into a given number of sectors to facilitate the organization of the operations to be ...

The Erdős-Sós conjecture says that a graph G on n vertices and number of edges e(G) > n(k− 1)/2 contains all trees of size k. In this paper we prove a sufficient condition for a graph to contain every tree of size k ...

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 ...

Bipartite graphs are combinatorial objects bearing some interesting symmetries. Thus, their spectra—eigenvalues of its adjacency matrix—are symmetric about zero, as the corresponding eigenvectors come into pairs. Moreover, ...

The Collatz conjecture is one of the most easy-to-state unsolved problems in Mathematics today. It states that after a finite number of iterations of the Collatz function, defined by C(n) = n/2 if n is even, and by C(n) = ...

We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result ...

Using methods from Analytic Combinatorics, we study the families of perfect matchings, partitions, chord diagrams, and hyperchord diagrams on a disk with a prescribed number of crossings. For each family, we express the ...