On some generalization of the Möbius configuration - Petelczyc, Krzysztof (Ars mathematica contemporanea, 2017)
The Möbius ?$(8_4)$? configuration is generalized in a purely combinatorial approach. We consider ?$(2n_n)$? configurations ?$\mathfrak{M}_{(n,φ)}$? depending on a permutation ?$φ$? in the symmetric group ?$S_n$?. Classes of non-isomorphic configurations of this type are determined. The parametric characterization of ?$\mathfrak{M}_{(n,φ)}$? is given. The uniqueness of the decomposition of ?$\mathfrak{M}_{(n,φ)}$? into two mutually inscribed ?$n$?-simplices is discussed. The automorphisms of ?$\mathfrak{M}_{(n,φ)}$? are characterized for ?$n≥ 3$?.
Keywords: konfiguracije; Möbiusova konfiguracija