A linear space S is said to be H-semiaffine if for any nonincident point-line pair (p,L) the number of lines through p which are disjoint to L is in H ; S is said to be H-affine if it is H-semiaffine but not H ′ -semiaffine for any proper subset H ′ of H . In this paper the authors manage to determine all (but finitely many) {1,3}-semiaffine linear spaces. It turns out that they are all naturally embeddable into a finite projective plane.
Finite {1,3} -semiaffine planes / Olanda, Domenico; N., Melone; A., Kersten. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - STAMPA. - 33:2(1984), pp. 225-232.
Finite {1,3} -semiaffine planes.
OLANDA, DOMENICO;
1984
Abstract
A linear space S is said to be H-semiaffine if for any nonincident point-line pair (p,L) the number of lines through p which are disjoint to L is in H ; S is said to be H-affine if it is H-semiaffine but not H ′ -semiaffine for any proper subset H ′ of H . In this paper the authors manage to determine all (but finitely many) {1,3}-semiaffine linear spaces. It turns out that they are all naturally embeddable into a finite projective plane.File in questo prodotto:
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