Artículo
Modular Schur numbers
Autor/es | Chappelon, Jonathan
Revuelta Marchena, María Pastora Sanz Domínguez, María Isabel |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2013 |
Fecha de depósito | 2022-09-01 |
Publicado en |
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Resumen | For any positive integers l and m, a set of integers is said to be (weakly) l-sum free modulo m if it contains no (pairwise distinct) elements x1, x2, . . . , xl
, y satisfying
the congruence x1 + . . . + xl ≡ y mod m. ... For any positive integers l and m, a set of integers is said to be (weakly) l-sum free modulo m if it contains no (pairwise distinct) elements x1, x2, . . . , xl , y satisfying the congruence x1 + . . . + xl ≡ y mod m. It is proved that, for any positive integers k and l, there exists a largest integer n for which the set of the first n positive integers {1, 2, . . . , n} admits a partition into k (weakly) l-sum-free sets modulo m. This number is called the generalized (weak) Schur number modulo m, associated with k and l. In this paper, for all positive integers k and l, the exact value of these modular Schur numbers are determined for m = 1, 2 and 3. |
Cita | Chappelon, J., Revuelta Marchena, M.P. y Sanz Domínguez, M.I. (2013). Modular Schur numbers. The Electronic Journal of Combinatorics, 20 (2) |
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