Defines the counting matrix K of a simplicial complex and establishes that it lies in SL(n,Z) with explicit inverse, positive definiteness, and spectral symmetry between K and its inverse.
Universality for Barycentric subdivision
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
The spectrum of the Laplacian of successive Barycentric subdivisions of a graph converges exponentially fast to a limit which only depends on the clique number of the initial graph and not on the graph itself. The proof uses an explicit linear operator mapping the clique vector of a graph to the clique vector of the Barycentric refinement. The eigenvectors of its transpose produce integral geometric invariants for which Euler characteristic is one example.
representative citing papers
An arbitrary integer energy function on a finite family of sets yields connection-style matrices whose determinant is the product of the energies and whose negative eigenvalue count matches the negative energy count.
The Moebius-Kantor graph MK is a Cayley graph for three non-abelian groups and admits a metric preserved uniquely by the Pauli group structure.
citing papers explorer
-
The counting matrix of a simplicial complex
Defines the counting matrix K of a simplicial complex and establishes that it lies in SL(n,Z) with explicit inverse, positive definiteness, and spectral symmetry between K and its inverse.
-
Energized simplicial complexes
An arbitrary integer energy function on a finite family of sets yields connection-style matrices whose determinant is the product of the energies and whose negative eigenvalue count matches the negative energy count.
-
Remarks about the Moebius-Kantor graph
The Moebius-Kantor graph MK is a Cayley graph for three non-abelian groups and admits a metric preserved uniquely by the Pauli group structure.