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APOLLONIAN STRUCTURE IN THE ABELIAN SANDPILE
APOLLONIAN STRUCTURE ABELIAN SANDPILE
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2015/8/14
The Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 neighbors. When begun f...
THE APOLLONIAN STRUCTURE OF INTEGER SUPERHARMONIC MATRICES
APOLLONIAN STRUCTURE INTEGER SUPERHARMONIC MATRICES
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2015/8/14
We prove that the set of quadratic growths attainable by integervalued superharmonic functions on the lattice Z2 has the structure of an Apollonian circle packing. This completely characterizes the PD...