Critical Groups of Simplicial Complexes

Critical Groups of Simplicial Complexes

We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of the critical group of a graph. We show how to realize these...

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Bibliographic Details
Main Authors: Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2011-01-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
graph
simplicial complex
critical group
combinatorial laplacian
chip-firing game
sandpile model
spanning trees
[math.math-co] mathematics [math]/combinatorics [math.co]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Online Access:https://dmtcs.episciences.org/2909/pdf

Internet

https://dmtcs.episciences.org/2909/pdf

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