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Bijection and Enumeration of Regions in Certain Coxeter Arrangements

Authors: Cao, Te;

Bijection and Enumeration of Regions in Certain Coxeter Arrangements

Abstract

We present here bijections between the regions of certain Type B, C, D Coxeter arrangements and certain configurations of trees. These bijections further allow us to obtain generating functions for the number of regions.

An n-dimensional real hyperplane arrangement is a finite collection of affine hyperplanesin R^n. A given arrangement separates R^n into disjoint regions and it is an important problem

The present work originates from an effort to generalise previously known methods andresults in Type A arrangements due to my advisor Olivier Bernardi in his previous work.

in combinatorics to understand these regions combinatorially, in particular to enumerate the

It should also serve as a starting point in developing a systematic bijective framework for

studying the combinatorics of general Coxeter arrangements.

number of regions associated to an arrangement.

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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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