Work

Sketches, Moves and Partitions: Counting Regions of Catalan Deformations of Reflection Arrangements

Year: 2025

Type: article

Abstract: The collection of reflecting hyperplanes of a finite Coxeter group is called a reflection arrangement and it appears in many subareas of combinatorics and representation theory. We focus on the problem of counting regions of reflection arrangements and their deformations. Inspired by the recent work of Bernardi, we show that the notion of moves and sketches can be used to provide a uniform and explicit bijection between regions of (the Catalan deformation of) a reflection arrangement and certain non-nesting partitions. We then use the exponential formula to describe a statistic on these partitions such that distribution is given by the coefficients of the characteristic polynomial. Finally, we consider a sub-arrangement of type C arrangement called the threshold arrangement and its Catalan and Shi deformations.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/13001

Authors: Priyavrat Deshpande, Krishna Menon

Institutions: Chennai Mathematical Institute, KTH Royal Institute of Technology

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Infosys Foundation

OpenAlex ID: W4414785406

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