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Bounds for arcs of arbitrary degree in finite desarguesian planes

journal contribution
posted on 2023-06-08, 23:45 authored by J W P Hirschfeld, E V D Pichanick
This paper examines subsets with at most n points on a line in the projective plane p q = PG(2, q). A lower bound for the size of complete (k, n)-arcs is established and shown to be a generalisation of a classical result by Barlotti. A sufficient condition ensuring that the trisecants to a complete (k, 3)-arc form a blocking set B in the dual plane p* q is provided. Finally, combinatorial arguments are used to show that, for q = 17, plane (k, 3)-arcs satisfying a prescribed incidence condition do not attain the best known upper bound.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Combinatorial Designs

ISSN

1063-8539

Publisher

John Wiley & Sons

Issue

4

Volume

24

Page range

184-196

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2015-12-15

First Compliant Deposit (FCD) Date

2015-12-15

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