Table of Contents
Journal of Discrete Mathematics
Volume 2014, Article ID 979171, 6 pages
http://dx.doi.org/10.1155/2014/979171
Research Article

On Some Numbers Related to Extremal Combinatorial Sum Problems

Dipartimento di Matematica e Informatica, Università della Calabria, Via Pietro Bucci, 87036 Arcavacata di Rende, Italy

Received 30 October 2013; Accepted 7 January 2014; Published 3 March 2014

Academic Editor: Franck Petit

Copyright © 2014 D. Petrassi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let n, d, and r be three integers such that . Chiaselotti (2002) defined as the minimum number of the nonnegative partial sums with d summands of a sum , where are n real numbers arbitrarily chosen in such a way that r of them are nonnegative and the remaining are negative. Chiaselotti (2002) and Chiaselotti et al. (2008) determine the values of for particular infinite ranges of the integer parameters n, d, and r. In this paper we continue their approach on this problem and we prove the following results: (i) for all values of n, d, and r such that ; (ii)