Proceedings of the American Mathematical Society

Author(s): Simeon Ball; Aart Blokhuis
Journal: Proc. Amer. Math. Soc. 126 (1998), 3377-3380.
MSC (1991): Primary 51E21; Secondary 05B25
Retrieve article in: PDF
This article is available free of charge

Abstract: It was a long-standing conjecture in finite geometry that a Desarguesian plane of odd order contains no maximal arcs. A rather inaccessible and long proof was given recently by the authors in collaboration with Mazzocca. In this paper a new observation leads to a greatly simplified proof of the conjecture.

1.: S. BALL, A. BLOKHUIS AND F. MAZZOCCA, Maximal arcs in Desarguesian planes of odd order do not exist, Combinatorica 17, (1997), 31-41. CMP 97:17
2.: A. COSSU, Su alcune proprietà dei $\{k;n\}$ -archi di un piano proiettivo sopra un corpo finito, Rend. Mat. e Appl., 20, (1961), 271-277. MR 25:3419
3.: R. H. F. DENNISTON, Some maximal arcs in finite projective planes, J. Combin. Theory, 6, (1969), 317-319. MR 39:1345
4.: L. RÉDEI, `Lückenhafte Polynome über endlichen Körpern, Birkhäuser Verlag, Basel (1970) (English translation: Lacunary polynomials over finite fields, North Holland, Amsterdam, 1973). MR 45:3366; MR 50:4548
5.: J. A. THAS, Construction of maximal arcs and partial geometries, Geom. Dedicata, 3, (1974), 61-64. MR 50:1931
6.: J. A. THAS, Some results concerning $\{ (q+1)(n-1);n \}-$ arcs and $\{ (q+1)(n-1)+1;n \}-$ arcs in finite projective planes of order $q$ , J. Combin. Theory Ser. A, 19, (1975), 228-232. MR 51:13851
7.: J. A. THAS, Construction of maximal arcs and dual ovals in translation planes, Europ. J. Combinatorics, 1, (1980), 189-192. MR 82a:05031

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 51E21, 05B25

Simeon Ball
Affiliation: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands

Aart Blokhuis
Affiliation: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands

DOI: 10.1090/S0002-9939-98-04653-X
PII: S 0002-9939(98)04653-X
Received by editor(s): March 23, 1997
Communicated by: Jeffry N. Kahn
Copyright of article: Copyright 1998, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS