On a Theorem of Deshouillers and Freiman

2013/09/23 by Balasubramanian, R., Pandey, Prem Prakash
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.5712

Abstract

The study of `structure' on subsets of abelian groups, with small `doubling constant', has been well studied in the last fifty years, from the time Freiman initiated the subject. In \citeDF Deshouillers and Freiman establish a structure theorem for subsets of \n with small doubling constant. In the current article we provide an alternate proof of one of the main theorem of \citeDF. Also our proof leads to slight improvement of the theorems in \citeDF.

Related

• Freiman's Theorem in an arbitrary abelian group
• On the number of sets with a given doubling constant
• Small doubling in groups
• Small doubling in groups with moderate torsion
• On sets with small doubling