Self-Inverses in Rauzy Classes

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dc.contributor.advisorVeech, William A.en_US
dc.creatorFickenscher, Jonathan Michaelen_US
dc.date.accessioned2012-07-03T22:49:47Zen_US
dc.date.available2012-07-03T22:49:47Zen_US
dc.date.created2011-04en_US
dc.date.issued2011en_US
dc.description.abstractThanks to works by M. Kontsevich and A. Zorich followed by C. Boissy, we have a classification of all Rauzy Classes of any given genus. It follows from these works that Rauzy Classes are closed under the operation of inverting the permutation. In this paper, we shall prove the existence of self-inverse permutations in every Rauzy Class by giving an explicit construction of such an element satisfying the sufficient conditions. As a corollary, we will give another proof that every Rauzy Class is closed under taking inverses. In the case of generalized permutations, generalized Rauzy Classes have been classified by works of M. Kontsevich, H. Masur and J. Smillie, E. Lanneau, and again C. Boissy. We state the definition of self-inverse for generalized permutations and prove a necessary and sufficient condition for a generalized Rauzy Class to contain self-inverse elements.en_US
dc.format.extent109 ppen_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationFickenscher, Jonathan Michael. "Self-Inverses in Rauzy Classes." (2011) Diss., Rice University. <a href="https://hdl.handle.net/1911/64435">https://hdl.handle.net/1911/64435</a>.en_US
dc.identifier.digitalFickenscherJen_US
dc.identifier.urihttps://hdl.handle.net/1911/64435en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.titleSelf-Inverses in Rauzy Classesen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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