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arXiv · 2412.02679

On z-Superstable and Critical Configurations of Chip Firing Pairs

Zach Benton·Jane Kwak·SuHo Oh·Mateo Torres·Mckinley Xie
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Abstract

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.

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Zach Benton, Jane Kwak, SuHo Oh, Mateo Torres, Mckinley Xie. 2025-06-13. On z-Superstable and Critical Configurations of Chip Firing Pairs. https://arxiv.org/abs/2412.02679

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