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Algebraic Limits of Sandpiles
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Abstract
The paper contributes to building algebraic foundations of self-organized criticality answering a previously unsolved question about the limiting structure of the extended sandpile group as well as relating it to another limit at the level of classical sandpile groups with respect to certain monomorphisms, and puts forward a concept of canonical sandpile epimorphisms, drawing unexpected consequences about the divisibility properties of the numbers of spanning trees for grid foldings.
Title: Algebraic Limits of Sandpiles
Description:
Abstract
The paper contributes to building algebraic foundations of self-organized criticality answering a previously unsolved question about the limiting structure of the extended sandpile group as well as relating it to another limit at the level of classical sandpile groups with respect to certain monomorphisms, and puts forward a concept of canonical sandpile epimorphisms, drawing unexpected consequences about the divisibility properties of the numbers of spanning trees for grid foldings.
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