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Pairings and related symmetry notions. (English) Zbl 1436.08001

A pairing is a triple \(\mathfrak{P} = (U, F,\Lambda)\), where \(U\) and \(\Lambda\) are non-empty sets and \(F : U \times \Omega \to \Lambda\) is a map. The authors show several examples of pairings for graphs, metric spaces, group actions and vector spaces with a given bilinear form. They reinterpret the notion of indiscernibility with respect to a given attribute set of information table on terms of local symmetry on \(U\). Then, they study so-called global version of symmetry which they call indistinguishability. They describe the symmetry transmission between subsets of \(\Omega\) and apply this concept for digraphs families.

MSC:

08A02 Relational systems, laws of composition
08A05 Structure theory of algebraic structures
06A06 Partial orders, general
06A05 Total orders
06A75 Generalizations of ordered sets
05C65 Hypergraphs
54A05 Topological spaces and generalizations (closure spaces, etc.)
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