Additive bases via Fourier analysis. (29th November 2021)

• Record Type: Journal Article
• Authors: Arsovski, Bodan
• Is Part Of: Combinatorics, probability and computing. Volume 30:Number 6(2021)
• Page Start: 930
• Page End: 941
• Publication Date: 2021-11-29
• Subjects: 11P99 -- 05E99; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548321000109
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract: Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c = c ( m ) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c ( m ) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.