Kirkman's tetrahedron and the fifteen schoolgirl problem
- Autori: Falcone, G.; Pavone, M.
- Anno di pubblicazione: 2011
- Tipologia: Articolo in rivista (Articolo in rivista)
- Parole Chiave: Kirkman triple systems, PG(3,2)
We give a visual construction of two solutions to Kirkman's fifteen schoolgirl problem by combining the fifteen simplicial elements of a tetrahedron. Furthermore, we show that the two solutions are nonisomorphic by introducing a new combinatorial algorithm. It turns out that the two solutions are precisely the two nonisomorphic arrangements of the 35 projective lines of PG(3,2) into seven classes of five mutually skew lines. Finally, we show that the two solutions are interchanged by the canonical duality of the projective space.