The simple incidence structure D(A, 2) formed by points and un-ordered pairs of distinct parallel lines of a finite affine plane A = (P,L) of order n > 2 is a 2 − (n^2, 2n, 2n − 1) design. If n = 3, D(A, 2) is the complementary design of A. If n = 4, D(A, 2) is isomorphic to the geometric design AG3(4, 2) (see [2; Theorem 1.2]). In this paper we give necessary and sufficient conditions for a 2−(n^2, 2n, 2n−1) design to be of the form D(A, 2) for some finite affine plane A of order n > 4. As a consequence we obtain a characterization of small designs D(A, 2).

CAGGEGI, A. (2004). Uniqueness of AG3(4,2). ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 15, 9-16.

Uniqueness of AG3(4,2)

CAGGEGI, Andrea
2004-01-01

Abstract

The simple incidence structure D(A, 2) formed by points and un-ordered pairs of distinct parallel lines of a finite affine plane A = (P,L) of order n > 2 is a 2 − (n^2, 2n, 2n − 1) design. If n = 3, D(A, 2) is the complementary design of A. If n = 4, D(A, 2) is isomorphic to the geometric design AG3(4, 2) (see [2; Theorem 1.2]). In this paper we give necessary and sufficient conditions for a 2−(n^2, 2n, 2n−1) design to be of the form D(A, 2) for some finite affine plane A of order n > 4. As a consequence we obtain a characterization of small designs D(A, 2).
2004
CAGGEGI, A. (2004). Uniqueness of AG3(4,2). ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 15, 9-16.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/32432
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