On the exterior algebra method applied to restricted set addition

Karolyi, Gyula and Paulin, Roland (2013) On the exterior algebra method applied to restricted set addition. European Journal of Combinatorics, 34 8: 1383-1389. doi:10.1016/j.ejc.2013.05.022


Author Karolyi, Gyula
Paulin, Roland
Title On the exterior algebra method applied to restricted set addition
Journal name European Journal of Combinatorics   Check publisher's open access policy
ISSN 0195-6698
1095-9971
Publication date 2013-11
Year available 2013
Sub-type Article (original research)
DOI 10.1016/j.ejc.2013.05.022
Volume 34
Issue 8
Start page 1383
End page 1389
Total pages 7
Place of publication Camden, London, United Kingdom
Publisher Academic Press
Collection year 2014
Language eng
Formatted abstract
In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of ErdÅ‘s and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A of the p-element group Z/pZ (where p is a prime), at least min{p,m|A|−m2 + 1} different elements of the group can be written as the sum of m different elements of A. In this note we present an easily accessible simplified version of their proof for the case m = 2, and explainhowthe method can be applied to obtain the corresponding inverse theorem.
Keyword Congruence Classes
Polynomial Method
Abelian Groups
Conjecture
Spaces
Sums
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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