{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:57Z","timestamp":1753893837728,"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>In this paper we consider the question how the set of inversions of a permutation $\\pi \\in S_n$ can be partitioned into two subsets, which are themselves inversion sets of permutations in $S_n$. Our method is to study the modular decomposition of the inversion graph of $\\pi$. A correspondence to the substitution decomposition of $\\pi$ is also given. Moreover, we consider the special case of multiplicative decompositions.<\/jats:p>","DOI":"10.37236\/2609","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:58:40Z","timestamp":1578711520000},"source":"Crossref","is-referenced-by-count":1,"title":["Decomposing Sets of Inversions"],"prefix":"10.37236","volume":"20","author":[{"given":"Lukas","family":"Katth\u00e4n","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,2,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:26:07Z","timestamp":1579260367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2609","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,2,25]]},"article-number":"P40"}}