{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T00:17:40Z","timestamp":1722557860965},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2008,1,8]],"date-time":"2008-01-08T00:00:00Z","timestamp":1199750400000},"content-version":"unspecified","delay-in-days":99,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Edinburgh Mathematical Society"],"published-print":{"date-parts":[[2007,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The symmetric inverse monoid $\\mathcal{I}_{n}$ is the set of all partial permutations of an $n$-element set. The largest possible size of a $2$-generated subsemigroup of $\\mathcal{I}_{n}$ is determined. Examples of semigroups with these sizes are given. Consequently, if $M(n)$ denotes this maximum, it is shown that $M(n)\/|\\mathcal{I}_{n}|\\rightarrow1$ as $n\\rightarrow\\infty$. Furthermore, we deduce the known fact that $\\mathcal{I}_{n}$ embeds as a local submonoid of an inverse $2$-generated subsemigroup of $\\mathcal{I}_{n+1}$.<\/jats:p>","DOI":"10.1017\/s0013091505001598","type":"journal-article","created":{"date-parts":[[2008,1,8]],"date-time":"2008-01-08T11:08:57Z","timestamp":1199790537000},"page":"551-561","source":"Crossref","is-referenced-by-count":4,"title":["LARGEST 2-GENERATED SUBSEMIGROUPS OF THE SYMMETRIC INVERSE SEMIGROUP"],"prefix":"10.1017","volume":"50","author":[{"given":"J. M.","family":"Andr\u00e9","sequence":"first","affiliation":[]},{"given":"V. H.","family":"Fernandes","sequence":"additional","affiliation":[]},{"given":"J. D.","family":"Mitchell","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,1,8]]},"container-title":["Proceedings of the Edinburgh Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0013091505001598","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T16:02:42Z","timestamp":1556726562000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0013091505001598\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,10]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,10]]}},"alternative-id":["S0013091505001598"],"URL":"https:\/\/doi.org\/10.1017\/s0013091505001598","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,10]]}}}