Symmetries of Arcs

Tim Penttila; C.M. O'Keefe

doi:10.1016/0097-3165(94)90050-7

Symmetries of Arcs

Tim Penttila, C.M. O'Keefe

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

Korchmaros has classified (q+2)-arcs of PG(2,q), q even, which have a transitive collineation stabiliser. In this paper we characterise (q + 1)-arcs, q-arcs, and (q - 1)-arcs of PG(2, q), q even, which have a transitive homography stabiliser as conics, translation q-arcs, and monomial (q - 1)-arcs, respectively (although for (q - 1)-arcs we need the hypothesis that q/4 is not a twelfth power). (C) 1994 Academic Press, Inc.

Original language	English
Pages (from-to)	53-67
Journal	Journal of Combinatorial Theory Series A
Volume	66
DOIs	https://doi.org/10.1016/0097-3165(94)90050-7
Publication status	Published - 1994

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title = "Symmetries of Arcs",

abstract = "Korchmaros has classified (q+2)-arcs of PG(2,q), q even, which have a transitive collineation stabiliser. In this paper we characterise (q + 1)-arcs, q-arcs, and (q - 1)-arcs of PG(2, q), q even, which have a transitive homography stabiliser as conics, translation q-arcs, and monomial (q - 1)-arcs, respectively (although for (q - 1)-arcs we need the hypothesis that q/4 is not a twelfth power). (C) 1994 Academic Press, Inc.",

author = "Tim Penttila and C.M. O'Keefe",

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T1 - Symmetries of Arcs

AU - Penttila, Tim

AU - O'Keefe, C.M.

PY - 1994

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N2 - Korchmaros has classified (q+2)-arcs of PG(2,q), q even, which have a transitive collineation stabiliser. In this paper we characterise (q + 1)-arcs, q-arcs, and (q - 1)-arcs of PG(2, q), q even, which have a transitive homography stabiliser as conics, translation q-arcs, and monomial (q - 1)-arcs, respectively (although for (q - 1)-arcs we need the hypothesis that q/4 is not a twelfth power). (C) 1994 Academic Press, Inc.

AB - Korchmaros has classified (q+2)-arcs of PG(2,q), q even, which have a transitive collineation stabiliser. In this paper we characterise (q + 1)-arcs, q-arcs, and (q - 1)-arcs of PG(2, q), q even, which have a transitive homography stabiliser as conics, translation q-arcs, and monomial (q - 1)-arcs, respectively (although for (q - 1)-arcs we need the hypothesis that q/4 is not a twelfth power). (C) 1994 Academic Press, Inc.

U2 - 10.1016/0097-3165(94)90050-7

DO - 10.1016/0097-3165(94)90050-7

M3 - Article

SN - 0097-3165

VL - 66

SP - 53

EP - 67

JO - Journal of Combinatorial Theory Series A

JF - Journal of Combinatorial Theory Series A

ER -

Symmetries of Arcs

Abstract

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