Inert matrices and matchings in partially oriented trees
We study inert matrices which remain degenerate or non-degenerate under any replacement of their non-zero elements by other non-zero numbers. In partially oriented graphs, we consider non-oriented matchings. We discuss a quantum model which fit these matchings. We prove that both perfect and imperfect oriented trees (that is, possessing and not possessing a perfect matching) may be obtained from the elementary ones with the use of some operations, that is, the set of the perfect trees and the set of the imperfect trees are free finitely generated algebraic structures.
This paper is concerned with 𝑝(≥2)-cyclic self-mappings 𝑇∶⋃𝑖∈𝑝𝐴𝑖→⋃𝑖∈𝑝𝐴𝑖 in a metric space (𝑋, 𝑑), with 𝐴𝑖⊂𝑋, 𝑇(𝐴𝑖)⊆𝐴𝑖