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Abelian networks III: The critical group [PDF]
Journal of Algebraic Combinatorics, 2015 The critical group of an abelian network is a finite abelian group that governs the behavior of the network on large inputs. It generalizes the sandpile group of a graph. We show that the critical group of an irreducible abelian network acts freely and transitively on recurrent states of the network.
Benjamin Bond, Lionel Levine
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Critical phenomena and renormalization-group theory [PDF]
Physics Reports, 2000 151 pages. Extended and updated version.
A. Pelissetto, E. Vicari
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The Critical Group of a Line Graph [PDF]
Annals of Combinatorics, 2009 The critical group of a graph is a finite abelian group whose order is the number of spanning forests of the graph. This paper provides three basic structural results on the critical group of a line graph.
A. Berget +4 more
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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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Exponent-critical groups [PDF]
Journal of Group TheoryWe define and investigate the property of being “exponent-critical” for a finite group. A finite group is said to be exponent-critical if its exponent is not the least common multiple of the exponents of its proper non-abelian subgroups.
Simon R. Blackburn +3 more
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On the critical group of the n-cube
Linear Algebra and its Applications, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hua Bai
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Chip-Firing and the Critical Group of a Graph [PDF]
Journal of Algebraic Combinatorics, 1999 Let \(G\) be a graph with perhaps multiple edges in which each vertex \(v\) is labeled with an integer \(s(v)\). A firing of a vertex is a modification of the vertex labeling increasing the label of each neighbor \(w\) of \(v\) by one for each edge between \(v\) and \(w\), and decreasing the label on \(v\) by the degree of \(v\) (essentially ...
N. Biggs
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Group interactions modulate critical mass dynamics in social convention [PDF]
Communications Physics, 2021 How can minorities of individuals overturn social conventions? The theory of critical mass states that when a committed minority reaches a critical size, a cascade of behavioural changes can occur, overturning apparently stable social norms.
Iacopo Iacopini +3 more
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Assessment of radiation exposure in the settlements located in Stepnogorsk area
Eurasian Journal of Physics and Functional Materials, 2021 The Stepnogorsk area Northern Kazakhstan has a long historymining activities. Mining activities have lots of environmental and health impacts. The aims of this study were to characterizing the general radiological situation of the area and evaluate ...
D. S. Ibrayeva +6 more
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Resonant problems for non-local elliptic operators with unbounded nonlinearites
Electronic Research Archive, 2023 In this paper we study the existence of nontrivial solutions of a class of asymptotically resonant problems driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions by applying Morse theory and critical groups ...
Yutong Chen, Jiabao Su
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