Quadrangle groups inclusions
interested only on those Fuchsian groups having fundamental regions of finite volume and generated by four elliptic elements, called quadrangle groups. We discuss the classification of all finite index inclusions between quadrangle groups obtained by generalising a result of Singerman (1972) on triangle groups.
From parking functions to the regions of the Shi arrangement
In the nineties Pak and Stanley introduced a labelling λ of the regions of the Shi arrangement with parking functions. In this talk we present an algorithm that returns a region R out of λ(R). This is done by relating λ to another bijection, that labels every region S of the braid arrangement with r(S), the unique central parking function f such that λ-1 (f) ⊆ S. In addition, we present a variant of the parking algorithm that is in the very origin of the term “parking function”.
This is joint work with António Guedes de Oliveira.