The bottom-triangle row-count conjecture for chip-firing configurations
The bottom-triangle row-count conjecture for chip-firing configurations
A configuration consists of rows of chips, with the bottom triangle formed by the minimal rows at the bottom of the configuration. Let the longest row be a row having maximal length among all rows in the configuration. Bottom-triangle row-count conjecture. The number of rows in the bottom triangle equals the length of the longest row minus . This is motivated by computations of for up to and including , which show that the intermediate configuration ends with a long rectangle followed by the bottom triangle, with the rectangle as its widest part. The claim remains conjectural beyond these computations.
Sources & referencesView supporting material
Primary source
Ryota Inagaki, Tanya Khovanova and Austin Luo, “Chip-firing on the Lattice of Nonnegative Integer Points”, arXiv:2601.09125 (2026).
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