Geodesic
Orientable self-embeddings of Steiner triple systems of order 15
Acta mathematica Universitatis Comenianae, Tome 75 (2006) no. 2 
G. K. Bennett; M. J. Grannell; T. S. Griggs. Orientable self-embeddings of Steiner triple systems of order 15. Acta mathematica Universitatis Comenianae, Tome 75 (2006) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2006_75_2_a2/
@article{AMUC_2006_75_2_a2,
     author = {G. K. Bennett and M. J. Grannell and T. S. Griggs},
     title = {Orientable self-embeddings of {Steiner} triple systems of order 15},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2006},
     volume = {75},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2006_75_2_a2/}
}
TY  - JOUR
AU  - G. K. Bennett
AU  - M. J. Grannell
AU  - T. S. Griggs
TI  - Orientable self-embeddings of Steiner triple systems of order 15
JO  - Acta mathematica Universitatis Comenianae
PY  - 2006
VL  - 75
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_2006_75_2_a2/
ID  - AMUC_2006_75_2_a2
ER  - 
%0 Journal Article
%A G. K. Bennett
%A M. J. Grannell
%A T. S. Griggs
%T Orientable self-embeddings of Steiner triple systems of order 15
%J Acta mathematica Universitatis Comenianae
%D 2006
%V 75
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2006_75_2_a2/
%F AMUC_2006_75_2_a2

Voir la notice de l'article provenant de la source Comenius University

It is shown that for 78 of the 80 isomorphism classes of Steiner triple systems of order 15 it is possible to find a face 2-colourable triangulation of the complete graph K 15 in an orientable surface in which the colour classes both form representatives of the specified isomorphism class. For one of the two remaining isomorphism classes it is proved that this is not possible. We also discuss the remaining open case. <br> <br><B>Keywords</b>: Additive inverse semiring, regular semiring, mutually inverse ideals. &nbsp