TY - JOUR
A2 - Petit, Franck
AU - Petrassi, D.
PY - 2014
DA - 2014/03/03
TI - On Some Numbers Related to Extremal Combinatorial Sum Problems
SP - 979171
VL - 2014
AB - Let n, d, and r be three integers such that 1 ≤ r , d ≤ n . Chiaselotti (2002) defined γ n , d , r as the minimum number of the nonnegative partial sums with d summands of a sum ∑ 1 = 1 n a i ≥ 0 , where a 1 , … , a n are n real numbers arbitrarily chosen in such a way that r of them are nonnegative and the remaining n - r are negative. Chiaselotti (2002) and Chiaselotti et al. (2008) determine the values of γ n , d , r 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) γ ( n , d , r ) ≤ ( r d ) + ( r d - 1 ) for all values of n, d, and r such that (d - 1) / d n - 1 ≤ r ≤ (d - 1) / d n ; (ii) γ d + 2 , d , d = d + 1 .
SN - 2090-9837
UR - https://doi.org/10.1155/2014/979171
DO - 10.1155/2014/979171
JF - Journal of Discrete Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -