On z-Superstable and Critical Configurations of Chip Firing Pairs

Fuente: arXiv
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Main Authors: Benton, Zach, Kwak, Jane, Oh, SuHo, Torres, Mateo, Xie, Mckinley
Format: Preprint
Published: 2024
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_version_ 1866916793080086528
author Benton, Zach
Kwak, Jane
Oh, SuHo
Torres, Mateo
Xie, Mckinley
author_facet Benton, Zach
Kwak, Jane
Oh, SuHo
Torres, Mateo
Xie, Mckinley
contents It is well known that there is a duality map between the superstable configurations and the critical configurations of a graph. This was extended to all M-matrices in (Guzmàn-Klivans 2015). We show a natural way to extend this to all $(L,M)$-chip firing pairs introduced in (Guzmàn-Klivans 2016). In addition, we study various properties of this map.
format Preprint
id arxiv_https___arxiv_org_abs_2412_02679
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On z-Superstable and Critical Configurations of Chip Firing Pairs
Benton, Zach
Kwak, Jane
Oh, SuHo
Torres, Mateo
Xie, Mckinley
Combinatorics
05C50, 05C22, 20K01, 91A46
It is well known that there is a duality map between the superstable configurations and the critical configurations of a graph. This was extended to all M-matrices in (Guzmàn-Klivans 2015). We show a natural way to extend this to all $(L,M)$-chip firing pairs introduced in (Guzmàn-Klivans 2016). In addition, we study various properties of this map.
title On z-Superstable and Critical Configurations of Chip Firing Pairs
topic Combinatorics
05C50, 05C22, 20K01, 91A46
url https://arxiv.org/abs/2412.02679