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Numerical renormalization group at criticality [PDF]
Physics Letters A, 1996 5 pages, LaTeX, 5 figures available upon ...
Tomotoshi Nishino +2 more
arxiv +5 more sources
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).
L. G. Kovács, Michael Newman
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Critical Groups of Simplicial Complexes [PDF]
Annals of Combinatorics, 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 group of a graph.
Duval, Art M. +2 more
openaire +7 more sources
Smith and Critical groups of Polar Graphs [PDF]
Journal of Combinatorial Theory, Series A, 2018 We compute the elementary divisors of the adjacency and Laplacian matrices of families of polar graphs. These graphs have as vertices the isotropic one-dimensional subspaces of finite vector spaces with respect to non-degenerate forms, with adjacency ...
Pantangi, Venkata Raghu Tej, Sin, Peter
core +3 more sources
Critical percolation of free product of groups [PDF]
International Journal of Algebra and Computation, 2008 In this article we study percolation on the Cayley graph of a free product of groups. The critical probability $p_c$ of a free product $G_1*G_2*...*G_n$ of groups is found as a solution of an equation involving only the expected subcritical cluster ...
Benjamini I. +6 more
core +7 more sources
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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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
Andrew Berget +4 more
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Diffeomorphism groups of critical regularity [PDF]
Inventiones mathematicae, 2020 AbstractLet M be a circle or a compact interval, and let $$\alpha =k+\tau \ge 1$$ α = k + τ ≥ 1 be a real number such that $$k=\lfloor \alpha \rfloor $$ k = ⌊ α ⌋ . We write $${{\,\mathrm{Diff}\,}}_+^{\alpha }(M)$$ Diff + α ( M ) for the group of orientation preserving $$C^k$$ C k diffeomorphisms of M whose kth derivatives are Hölder
Sang-hyun Kim, Thomas Koberda
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Differential posets and restriction in critical groups [PDF]
, 2019 In recent work, Benkart, Klivans, and Reiner defined the critical group of a faithful representation of a finite group $G$, which is analogous to the critical group of a graph.
Agarwal, Ayush, Gaetz, Christian
core +3 more sources
Critical groups of iterated cones [PDF]
Linear Algebra and its Applications, 2019 Let G be a finite graph, and let G_n be the n-th iterated cone over G. We study the structure of the critical group of G_n arising in divisor and sandpile theory.
David Perkinson, Gopal Goel
openaire +3 more sources