{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:05Z","timestamp":1753893845298,"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 introduce ballot matrices, a signed combinatorial structure whose\u00a0definition naturally follows from the generating function for labeled\u00a0interval orders. A sign reversing involution on ballot matrices is\u00a0defined. We show that matrices fixed under this involution are in\u00a0bijection with labeled interval orders and that they decompose to a\u00a0pair consisting of a permutation and an inversion table. To fully\u00a0classify such pairs, results pertaining to the enumeration of\u00a0permutations having a given set of ascent bottoms are given. This\u00a0allows for a new formula for the number of labeled interval orders.<\/jats:p>","DOI":"10.37236\/4360","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:53:55Z","timestamp":1578704035000},"source":"Crossref","is-referenced-by-count":0,"title":["Decomposing Labeled Interval Orders as Pairs of Permutations"],"prefix":"10.37236","volume":"21","author":[{"given":"Anders","family":"Claesson","sequence":"first","affiliation":[]},{"given":"Stuart A.","family":"Hannah","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,10,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:43:23Z","timestamp":1579257803000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i4p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4360","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,10,16]]},"article-number":"P4.16"}}