{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:29Z","timestamp":1753893869603,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>$S \\subseteq \\mathbb{Z}_{2n}$ is said to be sum-free if $S$ has no solution to the equation $a+b=c$. The sum-free process on $\\mathbb{Z}_{2n}$ starts with $S:=\\varnothing$, and iteratively inserts elements of $\\mathbb{Z}_{2n}$, where each inserted element is chosen uniformly at random from the set of all elements that could be inserted while maintaining that $S$ is sum-free. We prove a lower bound (which holds with high probability) on the final size of $S$, which matches a more general result of Bennett and Bohman, and also matches the order of a sharp threshold result proved by Balogh, Morris and Samotij. We also show that the set $S$ produced by the process has a particular non-pseudorandom property, which is in contrast with several known results about the random greedy independent set process on hypergraphs. <\/jats:p>","DOI":"10.37236\/8095","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:59:01Z","timestamp":1578617941000},"source":"Crossref","is-referenced-by-count":1,"title":["The Sum-Free Process"],"prefix":"10.37236","volume":"27","author":[{"given":"Patrick","family":"Bennett","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,1,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p13\/7998","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p13\/7998","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T22:59:40Z","timestamp":1579215580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8095","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,10]]},"article-number":"P1.13"}}