대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권3호
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  • Pages.733-746
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  • 2023
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2022.05.25
  • 심사 : 2022.10.11
  • 발행 : 2023.05.31
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⟨ 이전 논문 다음 논문 ⟩

초록

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).

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과제정보

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

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