Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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WHEN ALL PERMUTATIONS ARE COMBINATORIAL SIMILARITIES

  • Viktoriia Bilet (Department of Theory of Functions Institute of Applied Mathematics and Mechanics of NASU) ;
  • Oleksiy Dovgoshey (Department of Theory of Functions Institute of Applied Mathematics and Mechanics of NASU, Institut fuer Mathematik Universitaet zu Luebeck)
  • Received : 2022.05.25
  • Accepted : 2022.10.11
  • Published : 2023.05.31
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Abstract

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).

Keywords

Acknowledgement

The authors are grateful to the anonymous referee for useful comments and questions.

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