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A New Semifield Flock

A new semifield flock
Authors: BADER, LAURA; LUNARDON, GUGLIELMO; PINNERI I.;

A New Semifield Flock

Abstract

\textit{T. Penttila} and \textit{B. Williams} [Geom. Dedicata, to appear] have constructed a sporadic translation ovoid of the quadrangle \(Q(4, 3^5)\). Associated with this, there is a new (semifield) flock of a quadratic cone in \(\text{PG}(3,3^5)\), and hence a flock generalized quadrangle of order \((3^5,3^{10})\). The authors prove that this generalized quadrangle is new. Moreover, it is a translation generalized quadrangle, and also its translation dual is shown to be new. The exciting news about this is that it provides a counterexample to a conjecture recently stated by \textit{J. A. Thas} [J. Comb. Theory, Ser. A 79, No. 2, 223-254 (1997; Zbl 0887.51004)], saying that every semifield flock generalized quadrangle is known (classical, Kantor or Ganley).

Country
Italy
Keywords

flocks, good eggs, generalized quadrangle, ovoids, Theoretical Computer Science, Computational Theory and Mathematics, flock, Discrete Mathematics and Combinatorics, egg, Generalized quadrangles and generalized polygons in finite geometry, translation generalized quadrangles

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
24
Average
Top 10%
Top 10%
hybrid