{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:09Z","timestamp":1753893849956,"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>A pair $(\\mathcal{A},\\mathcal{B})$ of families of subsets of an $n$-element set is called cancellative if whenever $A,A'\\in\\mathcal{A}$ and $B\\in\\mathcal{B}$ satisfy $A\\cup B=A'\\cup B$, then $A=A'$, and whenever $A\\in\\mathcal{A}$ and $B,B'\\in\\mathcal{B}$ satisfy $A\\cup B=A\\cup B'$, then $B=B'$. It is known that there exist cancellative pairs with $|\\mathcal{A}||\\mathcal{B}|$ about $2.25^n$, whereas the best known upper bound on this quantity is $2.3264^n$. In this paper we improve this upper bound to $2.2682^n$. Our result also improves the best known upper bound for Simonyi's sandglass conjecture for set systems.<\/jats:p>","DOI":"10.37236\/7210","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:34:09Z","timestamp":1578670449000},"source":"Crossref","is-referenced-by-count":3,"title":["A New Upper Bound for Cancellative Pairs"],"prefix":"10.37236","volume":"25","author":[{"given":"Barnab\u00e1s","family":"Janzer","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,4,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:34:28Z","timestamp":1579235668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,27]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7210","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,4,27]]},"article-number":"P2.13"}}