ANOTHER PROOF OF WRIGHT'S INEQUALITIES

We present a short way of proving the inequalities obtained by Wright in [Journal of Graph Theory, 4: 393 - 407 (1980)] concerning the number of connected graphs with $\ell$ edges more than vertices

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.The second author was partially supported by Vicerrectorado de Investigación, Desarrollo e Innovación de la Universidad de Alicante under project GRE11-23

Strictness types: An inference algorithm and an application

This report deals with strictness types, a way of recording whether a function needs its argument(s) or not. We shall present an inference system for assigning strictness types to expressions and subsequently we transform this system into an algorithm capable of annotating expressions with strictness types. We give an example of a transformation which can be optimized by means of these annotations, and finally we prove the correctness of the optimized transformation – at the same time proving the correctness of the annotation. Everything has been implemented; documentation can be found in appendix