Hypercubes defined on \(n\)-ary sets, the Erdös-Faber-Lovász conjecture on graph coloring, and the description spaces of polypeptides and RNA. (English) Zbl 1429.92112
Summary: The present study deals with the possibility that \(N\)-dimensional hypercubes vertices could be constructed with chosen sets, composed by a given number of \(n\) elements. That is by: \(n\)-ary sets. Application of this possibility is discussed using as examples the coloring of graphs and the Erdös-Faber-Lovász conjecture, as well as protein and RNA descriptions. The outcome of this discussion induces a possibility to use \(p\)-dimensional hypercube vertices themselves as the possible elements of the \(n\)-ary sets as generators of \(N\)-dimensional hypercubes. Thus, providing: \(n = 2^p\).
Keywords:
\(n\)-ary \(N\)-dimensional hypercubes; \(N\)-dimensional hypercube generation; graph coloring; Erdös-Faber-Lovász conjecture; protein generator spaces; RNA generator spaces; unnatural proteins; unnatural RNAReferences:
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