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On a Divisibility Problem for Polynomials and its Application to Cameron–Praeger Designs
Author(s) -
Tuan Ngo Dac
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004241
Subject(s) - divisibility rule , mathematical economics , mathematics , algebra over a field , computer science , pure mathematics
Cameron–Praeger designs with parameters t −( v,k ,λ) are studied. Cameron and Praeger showed that in such designs, t = 2 or 3. In 1989, Delandtsheer and Doyen proved that if t = 2 thenv ⩽( (k2) − 1 ) 2 .In 2000, Mann and Tuan improved this equality and showed that if t = 3 thenv ⩽ (k2) + 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.