Artículo
Numerical semigroups of Szemerédi type
Autor/es | Adhikari, S. D.
Boza Prieto, Luis Eliahou, Shalom Revuelta Marchena, María Pastora Sanz Domínguez, María Isabel |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2019 |
Fecha de depósito | 2022-07-29 |
Publicado en |
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Resumen | Given any length k ≥ 3 and density 0 < δ ≤ 1, we introduce and study the set Sz(k, δ)
consisting of all positive integers n such that every subset of {1, 2, . . . , n} of density at
least δ contains an arithmetic progression ... Given any length k ≥ 3 and density 0 < δ ≤ 1, we introduce and study the set Sz(k, δ) consisting of all positive integers n such that every subset of {1, 2, . . . , n} of density at least δ contains an arithmetic progression of length k. A famous theorem of Szemerédi guarantees that this set is not empty. We show that Sz(k, δ)∪{0} is a numerical semigroup and we determine it for (k, δ) = (4, 1/2) and for more than thirty pairs (3, δ) with δ > 1/5. |
Cita | Adhikari, S.D., Boza Prieto, L., Eliahou, S., Revuelta Marchena, M.P. y Sanz Domínguez, M.I. (2019). Numerical semigroups of Szemerédi type. Discrete Applied Mathematics, 263 (June 2019), 8-13. |
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