1. Chip-Firing on Infinite $k$-ary Trees
- Author
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Agrawal, Dillan, Ge, Selena, Greene, Jate, Khovanova, Tanya, Kim, Dohun, Mandal, Rajarshi, Parida, Tanish, Pulugurtha, Anirudh, Redwine, Gordon, Samanta, Soham, and Xu, Albert
- Subjects
Mathematics - Combinatorics ,05C57, 05C63 - Abstract
We use an infinite $k$-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with $N$ chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given $k$ as a function of $N$ and study its properties. We do the same for the total number of fires., Comment: 22 pages, 1 figure
- Published
- 2025