Introduces q-spectrum and transition q-spectrum invariants for finite metric spaces that recover graph spectra in a limit and distinguish all spaces with at most 4 and 3 points respectively under stated conditions.
O'Hara, Magnitude function identifies generic finite metric spaces , to appear in Discrete Analysis, arXiv:2401.00786
2 Pith papers cite this work. Polarity classification is still indexing.
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Constructs homometric non-congruent circular metric spaces (some sharing magnitude), proves regular polygons are determined by distance multiset among planar spaces but not generally, and determines magnitude uniqueness for several n-gons and n-cycles.
citing papers explorer
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Spectral invariants of finite metric spaces
Introduces q-spectrum and transition q-spectrum invariants for finite metric spaces that recover graph spectra in a limit and distinguish all spaces with at most 4 and 3 points respectively under stated conditions.
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Distinguishing regular polygons, cycle graphs, and circular metric spaces by the distance multiset and magnitude
Constructs homometric non-congruent circular metric spaces (some sharing magnitude), proves regular polygons are determined by distance multiset among planar spaces but not generally, and determines magnitude uniqueness for several n-gons and n-cycles.