Each of the d-dimensional dual hyperovals S(m)(h) discovered by Yoshiara [20] gives rise, via affine expansion, to a flag-transitive semibiplane Af (S(m)(h)). We prove that, if m + h = d + 1, then Af (S(m)(h)) is an elation semibiplane. In the other cases, if d > 2 then Af (S(m)(h)) is not isomorphic to any of the examples we are aware of, except possibly for certain semibiplanes obtained from D(n)-buildings defined over G F(2). However, many semibiplanes live hidden as quotients inside halved hypercubes. It is thus quite natural to ask whether any of our semibiplanes are like that. We prove that Af (S(m)(h)) is a quotient of a halved hypercube if and only if h = m. (C) 2001 Academic Press.

Pasini, A., & Yoshiara, S. (2001). On a new family of flag-transitive semibiplanes. EUROPEAN JOURNAL OF COMBINATORICS, 22(4), 529-545 [10.1006/eujc.2001.0502].

On a new family of flag-transitive semibiplanes

PASINI, ANTONIO;
2001

Abstract

Each of the d-dimensional dual hyperovals S(m)(h) discovered by Yoshiara [20] gives rise, via affine expansion, to a flag-transitive semibiplane Af (S(m)(h)). We prove that, if m + h = d + 1, then Af (S(m)(h)) is an elation semibiplane. In the other cases, if d > 2 then Af (S(m)(h)) is not isomorphic to any of the examples we are aware of, except possibly for certain semibiplanes obtained from D(n)-buildings defined over G F(2). However, many semibiplanes live hidden as quotients inside halved hypercubes. It is thus quite natural to ask whether any of our semibiplanes are like that. We prove that Af (S(m)(h)) is a quotient of a halved hypercube if and only if h = m. (C) 2001 Academic Press.
Pasini, A., & Yoshiara, S. (2001). On a new family of flag-transitive semibiplanes. EUROPEAN JOURNAL OF COMBINATORICS, 22(4), 529-545 [10.1006/eujc.2001.0502].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/7072
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