Séminaire Lotharingien de Combinatoire, 93B.110 (2025), 12 pp.
Zach Benton, Jane Kwak, Suho Oh, Mateo Torres and Mckinley Xie
On z-Superstable and Critical Configurations of Chip-Firing Pairs
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 (Guzmán and Klivans, 2015). We show a natural way to extend this to all (L,M)-chip firing pairs introduced in (Guzmán and Klivans, 2016). In addition, we study various properties of z-superstable configurations and critical configurations of (L,M)-chip firing pairs.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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