{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T10:00:50Z","timestamp":1768730450259,"version":"3.49.0"},"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>Kasteleyn stated that the generating function of the perfect matchings of a graph of genus $g$ may be written as a linear combination of $4^g$ Pfaffians. Here we prove this statement. As a consequence we present a combinatorial way to compute the permanent of a square matrix.<\/jats:p>","DOI":"10.37236\/1438","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:01:53Z","timestamp":1578708113000},"source":"Crossref","is-referenced-by-count":48,"title":["On the Theory of Pfaffian Orientations.  I. Perfect Matchings and Permanents"],"prefix":"10.37236","volume":"6","author":[{"given":"Anna","family":"Galluccio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Loebl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1998,10,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:08:36Z","timestamp":1579327716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,10,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1438","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,10,28]]},"article-number":"R6"}}