%0 Journal Article 
%A Eliahou, Shalom
%A García García, Juan Ignacio
%A Marín Aragón, Daniel
%A Vigneron Tenorio, Alberto
%T The Buchweitz Set of a Numerical Semigroup
%D 2023
%@ 1678-7544
%U http://hdl.handle.net/10498/27845
%X Let A subset of Z be a finite subset. We denote by B(A) the set of all integers n >= 2 such that |nA|>(2n-1)(|A|-1), where nA=A+middotmiddotmiddot+A denotes the n-fold sumset of A. The motivation to consider B(A)stems from Buchweitz's discovery in 1980 that if a numerical semigroup S subset of N is a Weierstrass semigroup, then B(N\S)= empty set . By constructing instances where this condition fails, Buchweitz disproved a longstanding conjecture by Hurwitz (Math Ann 41:403-442, 1893). In this paper, we prove that for any numerical semigroup S subset of N of genus g >= 2, the set B(N\S) is finite, of unbounded cardinality as S varies.
%K Weierstrass numerical semigroup
%K Gapset
%K Additive combinatorics
%K Sumset growth
%K Freiman’s 3k
%K 3 theorem
%~ Universidad de Cádiz