Chip-firing groups of iterated cones

Morgan Brown; Jackson S. Morrow; David Zureick-Brown

doi:10.1016/j.laa.2018.06.023

Chip-firing groups of iterated cones

Morgan Brown, Jackson S. Morrow, David Zureick-Brown

Mathematics

Research output: Contribution to journal › Article

2 Scopus citations

Abstract

Let Γ be a finite graph and let Γ_n be the “nth cone over Γ” (i.e., the join of Γ and the complete graph K_n). We study the asymptotic structure of the chip-firing group Pic⁰(Γ_n).

Original language	English (US)
Pages (from-to)	46-54
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	556
DOIs	https://doi.org/10.1016/j.laa.2018.06.023
State	Published - Nov 1 2018

Keywords

Abelian sandpile
Chip-firing
Critical group
Graph Laplacian
Matrix-tree theorem

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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Brown, M., Morrow, J. S., & Zureick-Brown, D. (2018). Chip-firing groups of iterated cones. Linear Algebra and Its Applications, 556, 46-54. https://doi.org/10.1016/j.laa.2018.06.023

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abstract = "Let Γ be a finite graph and let Γn be the “nth cone over Γ” (i.e., the join of Γ and the complete graph Kn). We study the asymptotic structure of the chip-firing group Pic0(Γn).",

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KW - Critical group

KW - Graph Laplacian

KW - Matrix-tree theorem

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