Cardinality of Rauzy classes

Abstract

Rauzy classes define a partition of the set of irreducible (or indecomposable) permutations. They were defined by G. Rauzy as part of an induction algorithm for interval exchange transformations. In this article we prove an explicit formula for the cardinality of all Rauzy classes.

43 pages, 22 figures

References in corpus (1)

• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials

Cited by in corpus (2)

• Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata
• Labeled and Non-labeled Extended Rauzy Classes