6533b860fe1ef96bd12c3b0d
RESEARCH PRODUCT
Kirkman's tetrahedron and the fifteen schoolgirl problem
Giovanni FalconeMarco Pavonesubject
CombinatoricsGeneral Mathematics010102 general mathematics0103 physical sciencesKirkman triple systems PG(32)Tetrahedron010307 mathematical physicsSettore MAT/03 - Geometria0101 mathematics01 natural sciencesMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-12-01 |