@misc{10498/27845,
year = {2023},
month = {3},
url = {http://hdl.handle.net/10498/27845},
abstract = {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.},
publisher = {SPRINGER},
keywords = {Weierstrass numerical semigroup},
keywords = {Gapset},
keywords = {Additive combinatorics},
keywords = {Sumset growth},
keywords = {Freiman’s 3k},
keywords = {3 theorem},
title = {The Buchweitz Set of a Numerical Semigroup},
doi = {10.1007/s00574-022-00322-8},
author = {Eliahou, Shalom and García García, Juan Ignacio and Marín Aragón, Daniel and Vigneron Tenorio, Alberto},
}