{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T07:53:16Z","timestamp":1777362796055,"version":"3.51.4"},"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 semigroup is nilpotent of degree $3$ if it has a zero, every product of $3$ elements equals the zero, and some product of $2$ elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree $3$. We give formulae for the number of nilpotent semigroups of degree $3$ on a set with $n\\in\\mathbb{N}$ elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups on a set with $n$ elements up to equality and up to isomorphism.<\/jats:p>","DOI":"10.37236\/2441","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T07:19:49Z","timestamp":1578727189000},"source":"Crossref","is-referenced-by-count":10,"title":["The Number of Nilpotent Semigroups of Degree 3"],"prefix":"10.37236","volume":"19","author":[{"given":"Andreas","family":"Distler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. D.","family":"Mitchell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,6,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:33:08Z","timestamp":1579300388000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i2p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,28]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2441","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,28]]},"article-number":"P51"}}