Bounds on the cardinality of restricted sumsets in ℤ_p

2018/03/26 by Bengochea, Gabriel, Llano, Bernardo
#11B2 #11P99 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.09400

Abstract

In this paper we present a procedure which allows to transform a subset A of ℤ_p into a set A' such that |2\hspace0.15cm\widehat A'|≤|2\hspace0.15cm\widehat A | , where 2\hspace0.15cm\widehat A is defined to be the set \a+b:a≠ b, a,b∈ A\. From this result, we get some lower bounds for |2\hspace0.15cm\widehat A| . Finally, we give some remarks related to the problem for which sets A⊂ ℤ_p we have the equality |2\hspace0.15cm\widehat A|=2|A|-1.

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