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- W4298718802 abstract "The critical group of an abelian network is a finite abelian group that governs the behavior of the network on large inputs. It generalizes the sandpile group of a graph. We show that the critical group of an irreducible abelian network acts freely and transitively on recurrent states of the network. We exhibit the critical group as a quotient of a free abelian group by a subgroup containing the image of the Laplacian, with equality in the case that the network is rectangular. We generalize Dhar's burning algorithm to abelian networks, and estimate the running time of an abelian network on an arbitrary input up to a constant additive error." @default.
- W4298718802 created "2022-10-02" @default.
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- W4298718802 date "2014-08-30" @default.
- W4298718802 modified "2023-09-26" @default.
- W4298718802 title "Abelian networks III. The critical group" @default.
- W4298718802 doi "https://doi.org/10.48550/arxiv.1409.0170" @default.
- W4298718802 hasPublicationYear "2014" @default.
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