{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821769,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the problem of fast zeta and M\u00f6bius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and M\u00f6bius transforms can be computed in $O(e)$ elementary arithmetic operations, where $e$ denotes the size of the covering relation. We show that this family is exactly that of geometric lattices. We also extend the algorithms so that they work in $e$ operations for all semimodular lattices, including chains and divisor lattices. Finally, for both transforms, we provide a more general algorithm that works in $e$ operations for all ER-labelable posets.<\/jats:p>","DOI":"10.37236\/5998","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:27:11Z","timestamp":1578670031000},"source":"Crossref","is-referenced-by-count":2,"title":["Fast M\u00f6bius Inversion in Semimodular Lattices and ER-labelable Posets"],"prefix":"10.37236","volume":"23","author":[{"given":"Petteri","family":"Kaski","sequence":"first","affiliation":[]},{"given":"Jukka","family":"Kohonen","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Westerb\u00e4ck","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,8,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:17:01Z","timestamp":1579220221000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5998","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,8,19]]},"article-number":"P3.26"}}