Modular Schur numbers
| Autor: | Chappelon, Jonathan, Marchena, María Pastora Revuelta, Domínguez, María Isabel Sanz |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $x_1,x_2,...,x_l,y$ satisfying the congruence $x_1+\...+x_l\equiv y\bmod{m}$. 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. Comment: 25 pages, 3 tables |
| Databáze: | arXiv |
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