Geodesic
Coset geometries with trialities and their reduced incidence graphs
Dimitri Leemans1 ; Klara Stokes2 ; Dimitri Leemans ; Klara Stokes
1Département de Mathématique, C.P.216 -- Algèbre et Combinatoire, Université Libre de Bruxelles, Brussels, Belgium
2National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 911-916 
Dimitri Leemans; Klara Stokes; Dimitri Leemans; Klara Stokes. Coset geometries with trialities and their reduced incidence graphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 911-916. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a85/
@article{AMUC_2019_88_3_a85,
     author = {Dimitri Leemans and Klara Stokes and Dimitri Leemans and Klara Stokes},
     title = { Coset geometries with trialities and their reduced incidence graphs},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {911--916},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a85/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this article we explore combinatorial trialities and r-alities of incidence geometries. We give a construction that uses coset geometries to construct examples of incidence geometries with trialities and prescribed automorphism group. We define the reduced incidence graph of the geometry to be the oriented graph obtained as the quotient of the geometry under the triality, and more generally, under an r-ality. Our chosen examples exhibit interesting features relating the automorphism group of the geometry and the automorphism group of the reduced incidence graphs.