{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:15:36Z","timestamp":1759335336524,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a positive integer $n$, let $[n]$ denote $\\{1, \\ldots, n\\}$. For a 2-dimensional integer lattice point $\\mathbf{b}$ and positive integers $k\\geq 2$ and $n$, a $k$-sum $\\mathbf{b}$-free set\u00a0of $[n]\\times [n]$ is a subset $S$ of $[n]\\times [n]$ such that there are no elements $\\mathbf{a}_1, \\ldots, \\mathbf{a}_k$ in $S$ satisfying $\\mathbf{a}_1+\\cdots+\\mathbf{a}_k =\\mathbf{b}$. For a 2-dimensional integer lattice point $\\mathbf{b}$ and positive integers $k\\geq 2$ and $n$, we determine the maximum density of a $k$-sum $\\mathbf{b}$-free set\u00a0of $[n]\\times [n]$. This is the first investigation of the non-homogeneous sum-free set problem in higher dimensions.\u00a0<\/jats:p>","DOI":"10.37236\/8895","type":"journal-article","created":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T00:30:30Z","timestamp":1601598630000},"source":"Crossref","is-referenced-by-count":1,"title":["Maximum $k$-Sum $\\mathbf{n}$-Free Sets of the 2-Dimensional Integer Lattice"],"prefix":"10.37236","volume":"27","author":[{"given":"Ilkyoo","family":"Choi","sequence":"first","affiliation":[]},{"given":"Ringi","family":"Kim","sequence":"additional","affiliation":[]},{"given":"Boram","family":"Park","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,10,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p2\/8183","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p2\/8183","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T00:30:31Z","timestamp":1601598631000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,2]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/8895","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,10,2]]},"article-number":"P4.2"}}