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230
On the Sandpile Group of a Graph
 European Journal of Combinatorics
, 2000
"... We show how to express the sandpile model, introduced in theoretical physics, using the vocabulary of combinatorial theory. The group of recurrent configurations in the sandpile model, introduced by D. Dhar ([6]), may be considered as a finite abelian group associated with any graph G; we call it th ..."
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Cited by 10 (1 self)
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We show how to express the sandpile model, introduced in theoretical physics, using the vocabulary of combinatorial theory. The group of recurrent configurations in the sandpile model, introduced by D. Dhar ([6]), may be considered as a finite abelian group associated with any graph G; we call
SANDPILES AND DOMINOS
, 2014
"... We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular check ..."
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We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular
The sandpile group of a tree
 European J. Combin
"... Abstract. A wired tree is a graph obtained from a tree by collapsing the leaves to a single vertex. We describe a pair of short exact sequences relating the sandpile group of a wired tree to the sandpile groups of its principal subtrees. In the case of a regular tree these sequences split, enabling ..."
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Cited by 8 (4 self)
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Abstract. A wired tree is a graph obtained from a tree by collapsing the leaves to a single vertex. We describe a pair of short exact sequences relating the sandpile group of a wired tree to the sandpile groups of its principal subtrees. In the case of a regular tree these sequences split, enabling
On the Group of a Sandpile
 group, Discrete Math
"... The abelian sandpile model is a cellular automaton. Its rules generalize the sandpile rules for general graphs. This model has been introduced by Bak, Tang, and Wiesenfeld [1] in 1987. Dhar [9] showed that the set of recurrent configurations of this automaton has the structure of a finite abelian gr ..."
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Cited by 2 (0 self)
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The abelian sandpile model is a cellular automaton. Its rules generalize the sandpile rules for general graphs. This model has been introduced by Bak, Tang, and Wiesenfeld [1] in 1987. Dhar [9] showed that the set of recurrent configurations of this automaton has the structure of a finite abelian
Sandpile groups and spanning trees of directed line graphs
 J. Comb. Theory A
"... Abstract. We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted at a fixed vertex. In the case when ..."
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Cited by 14 (2 self)
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Abstract. We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted at a fixed vertex. In the case
Abelian Sandpile Model on Symmetric Graphs
, 2009
"... The abelian sandpile model, or chipfiring game, is a cellular automaton on finite directed graphs often used to describe the phenomenon of selforganized criticality. Here we present a thorough introduction to the theory of sandpiles. Additionally, we define a symmetric sandpile configuration, an ..."
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Cited by 2 (0 self)
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, and show that such configurations form a subgroup of the sandpile group. Given a graph, we explore the existence of a quotient graph whose sandpile group is isomorphic to the symmetric subgroup of the original graph. These explorations are motivated by possible applications to counting the domino tilings
Avalanches, Sandpiles and Tutte Decomposition
 In the Gelfand Mathematical Seminars, 19901992, Birkhauser
, 1993
"... ABSTRACT: Sandpile and avalanche models of failure were introduced recently (Bak et al., 1987, and an avalanche of publications with references to this paper) to simulate processes of different nature (earthquakes, charge density waves, forest fires, etc., including economics) characterized by self ..."
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Cited by 3 (0 self)
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organized critical behavior. Statistical properties of an important class of these models, Abelian sandpiles (Dhar, 1990) and Abelian avalanches (Gabrielov, 1992), can be investigated analytically due to an Abelian group acting on the phase space. It is shown that the distribution of avalanches in a discrete
Polynomial ideals for sandpiles and their Gröbner bases
, 2002
"... A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Gröbner basis of this ideal is interpreted combinatorially in terms of wellconnected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent ..."
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Cited by 19 (0 self)
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A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Gröbner basis of this ideal is interpreted combinatorially in terms of wellconnected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent
Results 1  10
of
230