The number of invariant factors of critical groups of arithmetical structures on a tree is bounded by a leaf-and-matching statistic, all trees whose arithmetical structures give only cyclic critical groups are classified, and every finite abelian group is realized as such a critical group on some…
Bishop, Alexander Diaz-Lopez, Luis D
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Generalized chip firing and critical groups of arithmetical structures on trees
The number of invariant factors of critical groups of arithmetical structures on a tree is bounded by a leaf-and-matching statistic, all trees whose arithmetical structures give only cyclic critical groups are classified, and every finite abelian group is realized as such a critical group on some…