TY - JOUR
T1 - On Eggs and Translation Generalised Quadrangles
AU - Lavrauw, M.
AU - Penttila, Tim
PY - 2001
Y1 - 2001
N2 - We study eggs in PG(4n - 1, q). A new model for eggs is presented in which all known examples are given. We calculate the general form of the dual egg for eggs arising from a semifield flock. Applying this to the egg obtained by L. Bader et al. (1999, J. Combin. Theory Ser. A 86, 49-62) from the Penttila-Williams ovoid, we obtain the dual egg, which is not isomorphic to any of the previous known examples. Furthermore we give a new proof of a conjecture of J. A. Thas (1994, J. Combin. Theory Ser. A 67, 140-160) using our model and classify all eggs of PG(7, 2) which is equivalent to the classification of all translation generalised quadrangles of order (4, 16). (C) 2001 Academic Press.
AB - We study eggs in PG(4n - 1, q). A new model for eggs is presented in which all known examples are given. We calculate the general form of the dual egg for eggs arising from a semifield flock. Applying this to the egg obtained by L. Bader et al. (1999, J. Combin. Theory Ser. A 86, 49-62) from the Penttila-Williams ovoid, we obtain the dual egg, which is not isomorphic to any of the previous known examples. Furthermore we give a new proof of a conjecture of J. A. Thas (1994, J. Combin. Theory Ser. A 67, 140-160) using our model and classify all eggs of PG(7, 2) which is equivalent to the classification of all translation generalised quadrangles of order (4, 16). (C) 2001 Academic Press.
U2 - 10.1006/jcta.2001.3179
DO - 10.1006/jcta.2001.3179
M3 - Article
SN - 0097-3165
VL - 96
SP - 303
EP - 315
JO - Journal of Combinatorial Theory Series A
JF - Journal of Combinatorial Theory Series A
ER -