Methodology Seminar
Date and Time: 3.30 PM, Monday, 11.04.2022.
A branch statistic for trees
Krishna Menon
Chennai Mathematical Institute.
11-04-22

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Abstract

A hyperplane arrangement is a finite collection of affine hyperplanes in Euclidean space. Its regions are the connected components of the complement of these hyperplanes. By a theorem of Zaslavsky, the number of regions of a hyperplane arrangement is the sum of coefficients of its characteristic polynomial. In this talk, we study an important class of arrangements called extended Catalan arrangements. The regions of such arrangements are known to correspond to certain labeled trees. We define a statistic on these trees such that its distribution is given by the coefficients of the characteristic polynomial. This is joint work with Priyavrat Deshpande.