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A presentation for the monoid of uniform block bijections
This is the author's preprint version, which differs from the published version in having an older address, and omitting an introductory paragraph and a reference, added in proof, to M. Kosuda, Ryuku Math. J.13 (2000) 7-22." name="eprints.note" />
<meta content=" The monoid Fn of uniform block bijections is the factorizable inverse monoid
which arises from the natural action of the symmetric group on the join
semilattice of equivalences on an n-set; it has been described in the literature as the factorizable part of the dual symmetric inverse monoid. The
present paper gives and proves correct a monoid presentation for Fn: The
methods involved make use of a general criterion for a monoid generated by
a group and an idempotent to be inverse, the structure of factorizable inverse
monoids, and presentations of the symmetric group and the join semilattice
of equivalences on an n-set." name="eprints.abstract" />
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<meta content="[1] S. Y. Chen and S. C. Hsieh, `Factorizable inverse semigroups', Semigroup Forum 8 (1984) 283-297.
[2] D. G. FitzGerald and Jonathan Leech, `Dual symmetric inverse monoids and representation theory', J. Austral. Math. Soc. (Series A) 64 (1998) 345-367.
[3] P. A. Grillet, Semigroups: an introduction to the structure theory
(Marcel Dekker, New York, 1995).
[4] M. V. Lawson, Inverse semigroups: the theory of partial symmetries
(World Scientific, Singapore, 1998).
[5] E. H. Moore, `Concerning the abstract groups of order k! and (()/1)2k! holohedrically isomorphic with the symmetric and alternating substitution groups on k letters', Proc. London Math. Soc. 28 (1897) 357-366.
[6] L. M. Popova, `Defining relations in some semigroups of partial transformations of a finite set', Uchenye Zap. Leningrad. Gos. Ped. Inst. 218 (1961) 191-212 (in Russian)." name="eprints.referencetext" />
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<meta content=" The monoid Fn of uniform block bijections is the factorizable inverse monoid
which arises from the natural action of the symmetric group on the join
semilattice of equivalences on an n-set; it has been described in the literature as the factorizable part of the dual symmetric inverse monoid. The
present paper gives and proves correct a monoid presentation for Fn: The
methods involved make use of a general criterion for a monoid generated by
a group and an idempotent to be inverse, the structure of factorizable inverse
monoids, and presentations of the symmetric group and the join semilattice
of equivalences on an n-set." name="DC.description" />
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<h1 class="ep_tm_pagetitle">A presentation for the monoid of uniform block permutations</h1>
<p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">FitzGerald, D.G.</span> (2003) <xhtml:em>A presentation for the monoid of uniform block permutations.</xhtml:em> Bulletin of the Australian Mathematical Society, 68 . pp. 317-324. ISSN 0004-9727</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a href="http://eprints.utas.edu.au/1900/1/ubb4.pdf"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" border="0" class="ep_doc_icon" /></a></td><td valign="top"><a href="http://eprints.utas.edu.au/1900/1/ubb4.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />139Kb</td><td><form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/request_doc"><input value="2395" name="docid" accept-charset="utf-8" type="hidden" /><div class=""><input value="Request a copy" name="_action_null" class="ep_form_action_button" onclick="return EPJS_button_pushed( '_action_null' )" type="submit" /> </div></form></td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://www.austms.org.au/Publ/Bulletin/">http://www.austms.org.au/Publ/Bulletin/</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto"> The monoid Fn of uniform block bijections is the factorizable inverse monoid
which arises from the natural action of the symmetric group on the join
semilattice of equivalences on an n-set; it has been described in the literature as the factorizable part of the dual symmetric inverse monoid. The
present paper gives and proves correct a monoid presentation for Fn: The
methods involved make use of a general criterion for a monoid generated by
a group and an idempotent to be inverse, the structure of factorizable inverse
monoids, and presentations of the symmetric group and the join semilattice
of equivalences on an n-set.</p></div><table style="margin-bottom: 1em" border="0" cellpadding="3" class="not_ep_block"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Article</td></tr><tr><th valign="top" class="ep_row">Additional Information:</th><td valign="top" class="ep_row">Different title on PDF
A presentation for the monoid of uniform block bijections
This is the author's preprint version, which differs from the published version in having an older address, and omitting an introductory paragraph and a reference, added in proof, to M. Kosuda, Ryuku Math. J.13 (2000) 7-22.</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">inverse semigroups, factorizable inverse monoids, generators and relations</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/230105.html">230000 Mathematical Sciences > 230100 Mathematics > 230105 Group Theory And Generalisations (Incl. Topological Groups And Lie Groups)</a></td></tr><tr><th valign="top" class="ep_row">Collections:</th><td valign="top" class="ep_row">UNSPECIFIED</td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">1900</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Dr D. G. FitzGerald</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">12 Sep 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">07 Feb 2008 12:13</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=1900;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&eprintid=1900">item control page</a></p>
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