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ON A DIVISIBILITY PROBLEM FOR POLYNOMIALS AND ITS APPLICATION TO CAMERON–PRAEGER DESIGNS

Published online by Cambridge University Press:  20 May 2003

NGO DAC TUAN
NGO DAC TUAN
Affiliation:
Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, F-91405 Orsay Cedex, Francetuan.ngo-dac@polytechnique.org
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Abstract

Cameron–Praeger designs with parameters $t-(v,k,\lambda)$ are studied. Cameron and Praeger showed that in such designs, $t=2$ or 3. In 1989, Delandtsheer and Doyen proved that if $t=2$ then \[ v \leqslant \left(\left({k \atop 2}\right)-1\right)^2. \] In 2000, Mann and Tuan improved this equality and showed that if $t=3$ then \[ v \leqslant \left({k \atop 2}\right)+1. \] Three infinite families of Cameron–Praeger 3-designs for which this bound is met have been constructed by Mann and Tuan and by Sebille. The paper constructs infinitely many infinite families of such Cameron–Praeger 3-designs via a study of a divisibility problem for polynomials. Further, the construction generalizes the previous constructions.

Keywords

05B0512D9951E05
Type
Research Article
Information
Journal of the London Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 545 - 560
Copyright
The London Mathematical Society 2003

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