# Refinements of the braid arrangement and two parameter Fuss-Catalan numbers

@inproceedings{Deshpande2022RefinementsOT, title={Refinements of the braid arrangement and two parameter Fuss-Catalan numbers}, author={Priyavrat Deshpande and Krishna Menon and Writika Sarkar}, year={2022} }

A hyperplane arrangement inR is a finite collection of affine hyperplanes. Counting regions of hyperplane arrangements is an active research direction in enumerative combinatorics. In this paper, we consider the arrangement A n in R given by {xi = 0 | i ∈ [n]} ∪ {xi = a xj | k ∈ [−m,m], 1 ≤ i < j ≤ n} for some fixed a > 1. It turns out that this family of arrangements is closely related to the well-studied extended Catalan arrangement of type A. We prove that the number of regions of A n is a…

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