We construct an infinite family of one-factorizations of K_v admitting an automorphism group acting primitively on the set ofvertices but no such group acting doubly transitively. We also give examples of one-factorizations which are live, in the sense that every one-factor induces an automorphism, but do not coincide with the affine line parallelism of AG(n, 2). To this purpose we develop the notion of a “mixed translation” in AG(n, 2).
Primitive one-factorizations and the geometry of mixed translations / Bonisoli, Arrigo; Bonvicini, Simona. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 308:5-6(2008), pp. 726-733. [10.1016/j.disc.2007.07.058]
Primitive one-factorizations and the geometry of mixed translations
BONISOLI, Arrigo;BONVICINI, Simona
2008
Abstract
We construct an infinite family of one-factorizations of K_v admitting an automorphism group acting primitively on the set ofvertices but no such group acting doubly transitively. We also give examples of one-factorizations which are live, in the sense that every one-factor induces an automorphism, but do not coincide with the affine line parallelism of AG(n, 2). To this purpose we develop the notion of a “mixed translation” in AG(n, 2).
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