{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:44Z","timestamp":1753893824684,"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>We count the ordered sum-free triplets of subsets in the group $\\mathbb{Z}\/p\\mathbb{Z}$, i.e., the triplets $(A,B,C)$ of sets $A,B,C \\subset\u00a0\\mathbb{Z}\/p\\mathbb{Z}$ for which the equation $a+b=c$ has no solution with $a\\in A$, $b \\in B$ and $c \\in C$. Our main theorem improves on a recent result by Semchankau, Shabanov, and Shkredov using a different and simpler method. Our proof relates previous results on the number of independent sets of regular graphs by Kahn; Perarnau and Perkins; and Csikv\u00e1ri to produce explicit estimates on smaller order terms. We also obtain estimates for the number of sum-free triplets of subsets in a general abelian group.\u00a0<\/jats:p>","DOI":"10.37236\/10170","type":"journal-article","created":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T02:05:27Z","timestamp":1638497127000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Number of Sum-Free Triplets of Sets"],"prefix":"10.37236","volume":"28","author":[{"given":"Igor","family":"Araujo","sequence":"first","affiliation":[]},{"given":"J\u00f3zsef","family":"Balogh","sequence":"additional","affiliation":[]},{"given":"Ramon","family":"I. Garcia","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,12,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T02:05:28Z","timestamp":1638497128000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i4p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,3]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,10,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10170","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,12,3]]},"article-number":"P4.36"}}