RT journal article
T1 The Buchweitz Set of a Numerical Semigroup
A1 Eliahou, Shalom
A1 García García, Juan Ignacio
A1 Marín Aragón, Daniel
A1 Vigneron Tenorio, Alberto
A2 Matemáticas
K1 Weierstrass numerical semigroup
K1 Gapset
K1 Additive combinatorics
K1 Sumset growth
K1 Freiman’s 3k
K1 3 theorem
AB 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.
PB SPRINGER
SN 1678-7544
YR 2023
FD 2023-03
LK http://hdl.handle.net/10498/27845
UL http://hdl.handle.net/10498/27845
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026