2012/12/30 by Jon Fickenscher, Fickenscher, Jon
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1212.6742
openalex publication_date 2012/12/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Rauzy Classes and Extended Rauzy Classes are equivalence classes of\npermutations that arise when studying Interval Exchange Transformations. In\n2003, Kontsevich and Zorich classified Extended Rauzy Classes by using data\nfrom Translation Surfaces, which are associated to IET's thanks to the Zippered\nRectangle Construction of Veech from 1982. In 2009, Boissy finalized the\nclassification of Rauzy Classes also using information from Translation\nSurfaces. We present in this paper specialized moves in (Extended) Rauzy\nClasses that allows us to prove the sufficiency and necessity in the previous\nclassification theorems. These results provide a complete, and purely\ncombinatorial, proof of these known results. We end with some general\nstatements about our constructed move.\n