{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T05:45:03Z","timestamp":1757310303754,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $x_1,x_2,\\ldots,x_l,y$ satisfying the congruence $x_1+\\ldots+x_l\\equiv y\\bmod{m}$. 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 $\\{1,2,\\ldots,n\\}$ 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 $3$.<\/jats:p>","DOI":"10.37236\/2374","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:24:44Z","timestamp":1578705884000},"source":"Crossref","is-referenced-by-count":1,"title":["Modular Schur Numbers"],"prefix":"10.37236","volume":"20","author":[{"given":"Jonathan","family":"Chappelon","sequence":"first","affiliation":[]},{"given":"Mar\u00eda Pastora","family":"Revuelta Marchena","sequence":"additional","affiliation":[]},{"given":"Mar\u00eda Isabel","family":"Sanz Dom\u00ednguez","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,6,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p61\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p61\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:16:58Z","timestamp":1579259818000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p61"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,30]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/2374","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,6,30]]},"article-number":"P61"}}