Results 1 to 10 of about 222 (138)
On the sandpile model of modified wheels II
Open Mathematics, 2020 We investigate the abelian sandpile group on modified wheels Wˆn{\hat{W}}_{n} by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45].
Zahid Raza, Mohammed M M Jaradat
exaly +2 more sources
Harmonic dynamics of the abelian sandpile [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2019 Moritz Lang, Mikhail Shkolnikov
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Rotor-Routing Induces the Only Consistent Sandpile Torsor Structure on Plane Graphs
Forum of Mathematics, Sigma, 2023 We make precise and prove a conjecture of Klivans about actions of the sandpile group on spanning trees. More specifically, the conjecture states that there exists a unique ‘suitably nice’ sandpile torsor structure on plane graphs which is induced by ...
Ankan Ganguly, Alex McDonough
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Sandpile monomorphisms and limits
Comptes Rendus. Mathématique, 2022 We introduce a tiling problem between bounded open convex polyforms $\hat{P}\subset \mathbb{R}^2$ with colored directed edges. If there exists a tiling of the polyform $\hat{P}_2$ by $\hat{P}_1$, we construct a monomorphism from the sandpile group $G_ ...
Lang, Moritz, Shkolnikov, Mikhail
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The sandpile group of a thick cycle graph
Electronic Journal of Graph Theory and Applications, 2022 The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted.
Diane Christine Alar +4 more
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British Educational Research Journal, EarlyView., 2023 Abstract Children's relationship with time in preschools is an under‐researched area. Young children rarely know how to measure time using a clock, but their experiences of time may contribute to understanding children's well‐being and debates about quality in preschools.
Kristín Dýrfjörð +3 more
wiley +1 more source
Chip-Firing and Rotor-Routing on $\mathbb{Z}^d$ and on Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 The sandpile group of a graph $G$ is an abelian group whose order is the number of spanning trees of $G$. We find the decomposition of the sandpile group into cyclic subgroups when $G$ is a regular tree with the leaves are collapsed to a single vertex ...
Itamar Landau +2 more
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Firing Patterns in the Parallel Chip-Firing Game [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 The $\textit{parallel chip-firing game}$ is an automaton on graphs in which vertices "fire'' chips to their neighbors. This simple model, analogous to sandpiles forming and collapsing, contains much emergent complexity and has connections to different ...
Ziv Scully, Tian-Yi Jiang, Yan Zhang
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Homomesy in products of two chains [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Many cyclic actions $τ$ on a finite set $\mathcal{S}$ ; of combinatorial objects, along with a natural statistic $f$ on $\mathcal{S}$, exhibit ``homomesy'': the average of $f$ over each $τ$-orbit in $\mathcal{S} $ is the same as the average of $f$ over ...
James Propp, Tom Roby
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Critical Groups of Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of the critical ...
Art M. Duval +2 more
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