Chip-firing groups of iterated cones

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

doi:10.1016/j.laa.2018.06.023

Chip-firing groups of iterated cones

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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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10.1016/j.laa.2018.06.023

Cite this

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title = "Chip-firing groups of iterated cones",

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).",

keywords = "Abelian sandpile, Chip-firing, Critical group, Graph Laplacian, Matrix-tree theorem",

author = "Brown, {Morgan V.} and Morrow, {Jackson S.} and David Zureick-Brown",

year = "2018",

month = nov,

day = "1",

doi = "10.1016/j.laa.2018.06.023",

language = "English (US)",

volume = "556",

pages = "46--54",

journal = "Linear Algebra and Its Applications",

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publisher = "Elsevier Inc.",

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TY - JOUR

T1 - Chip-firing groups of iterated cones

AU - Brown, Morgan V.

AU - Morrow, Jackson S.

AU - Zureick-Brown, David

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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).

AB - 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).

KW - Abelian sandpile

KW - Chip-firing

KW - Critical group

KW - Graph Laplacian

KW - Matrix-tree theorem

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DO - 10.1016/j.laa.2018.06.023

M3 - Article

AN - SCOPUS:85049468238

VL - 556

SP - 46

EP - 54

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Chip-firing groups of iterated cones

Abstract

Keywords

ASJC Scopus subject areas

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