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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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Eigenvalues and critical groups of Adinkras
Advances in Applied Mathematics, 2023 Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction to these objects, and study the properties of their signed adjacency and signed Laplacian matrices. These matrices each have exactly two distinct eigenvalues (of equal multiplicity), making Adinkras closely related to the notions of strongly regular graphs. We
Iga, Kevin +3 more
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Resonant Anisotropic (p,q)-Equations
Mathematics, 2020 We consider an anisotropic Dirichlet problem which is driven by the (p(z),q(z))-Laplacian (that is, the sum of a p(z)-Laplacian and a q(z)-Laplacian), The reaction (source) term, is a Carathéodory function which asymptotically as x±∞ can be resonant with
Leszek Gasiński +1 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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Nonlinear resonant problems with an indefinite potential and concave boundary condition
Electronic Journal of Qualitative Theory of Differential Equations, 2020 We consider a nonlinear elliptic problem driven by the $p$-Laplacian plus and indefinite potential term. The reaction is $(p-1)$-linear and resonant and the boundary term is concave. The problem is nonparametric.
Nikolaos Papageorgiou, Andrea Scapellato
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Journal of the Australian Mathematical Society, 1966 The concept of critical group was introduced by D. C. Cross (as reported byG. Higman in [5]): a finite group is calledcriticalif it is not contained in the variety generated by its proper factors. (Thefactorsof a groupGare the groups H/K where KH ≦G, and H/K is aproper factorofGunlessH = GandK=1).
Kovacs, L. G., Newman, M. F.
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Cuts and Flows of Cell Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study the vector spaces and integer lattices of cuts and flows of an arbitrary finite CW complex, and their relationships to its critical group and related invariants.
Art M. Duval +2 more
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Numerical renormalization group at criticality [PDF]
Physics Letters A, 1996 5 pages, LaTeX, 5 figures available upon ...
Nishino, T., Okunishi, K., Kikuchi, M.
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Cyclic Critical Groups of Graphs [PDF]
Australas. J Comb., 2015 In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the group exactly. We also pose several open questions related to this work.
Ryan Becker, Darren B. Glass
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The Critical Group of a Line Graph [PDF]
Annals of Combinatorics, 2012 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. The first deals with connected graphs containing no cut-edge. Here the number of independent cycles in the graph, which is known to bound the number
Berget, Andrew +4 more
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