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dc.contributor.advisor Veech, William A.
dc.creatorFickenscher, Jonathan Michael
dc.date.accessioned 2012-07-03T22:49:47Z
dc.date.available 2012-07-03T22:49:47Z
dc.date.created 2011-04
dc.date.issued 2011
dc.identifier.urihttp://hdl.handle.net/1911/64435
dc.description.abstract Thanks 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.
dc.format.extent 109 pp
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title Self-Inverses in Rauzy Classes
dc.identifier.digital FickenscherJ
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Fickenscher, Jonathan Michael. "Self-Inverses in Rauzy Classes." (2011) PhD diss., Rice University. http://hdl.handle.net/1911/64435.


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