• Title/Summary/Keyword: strongly rigid metric

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WHEN ALL PERMUTATIONS ARE COMBINATORIAL SIMILARITIES

  • Viktoriia Bilet;Oleksiy Dovgoshey
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.733-746
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    • 2023
  • Let (X, d) be a semimetric space. A permutation Φ of the set X is a combinatorial self similarity of (X, d) if there is a bijective function f : d(X × X) → d(X × X) such that d(x, y) = f(d(Φ(x), Φ(y))) for all x, y ∈ X. We describe the set of all semimetrics ρ on an arbitrary nonempty set Y for which every permutation of Y is a combinatorial self similarity of (Y, ρ).