On the existence of distinct lengths zero-sum subsequences
Year: 2009
Type: preprint
Abstract: In this note, we obtain a characterization of short normal sequences in a finite Abelian p-group, thus answering positively a conjecture of W. Gao for a variety of such groups. Our main result is deduced from a theorem of N. Alon, S. Friedland and G. Kalai, originally proved so as to study the existence of regular graphs in almost regular graphs. In the special case of elementary p-groups, Gao’s conjecture is solved using N. Alon’s Combinatorial Nullstellensatz.
Source: arXiv (Cornell University)
Author: Benjamin Girard
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1704196922