2026-09-21T06:06:58Zhttps://repository.rice.edu/server/oai/request

oai:repository.rice.edu:1911/644352024-01-11T20:58:22Zcom_1911_8299col_1911_13110

Veech, William A. Fickenscher, Jonathan Michael 2012-07-03T22:49:47Z 2012-07-03T22:49:47Z 2011-04 2011 Fickenscher, 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>. https://hdl.handle.net/1911/64435 FickenscherJ 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. 109 pp application/pdf eng Copyright 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. Mathematics Self-Inverses in Rauzy Classes Thesis Text Mathematics Natural Sciences Rice University Doctoral Doctor of Philosophy open.access