Breadcrumb
Combinatorial generalization of interval exchange transformations and cluster combinatorics
Wed 06 March 2013, 14:30
Sibylle Schroll
University of Leicester
Organisers: Tony Skyner, Neil Saunders
ABSTRACT
We develop and study the structure of combinatorial objects related to interval exchange transformations, generalising work of Cassaigne, Ferenczi and Zamboni. We show how the dynamical notion of induction can be generalised to these objects and show that a natural subset is in bijection with a set of m-clusters in the sense of Fomin-Reading. We then show how the induction procedure in this correspondence corresponds to a composition of combinatorial cluster mutations, that is how it corresponds to a series of rotations of diagonals in an m-angulation of a polygon. (This is joint work with R. Marsh).