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Locally resolvable BIBDs and generalized quadrangles with ovoids

Ryan McCulloch
Vol. 21 (2024), No. 1, 131–137
DOI: 10.2140/iig.2024.21.131
Abstract

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that possess a nontriangular local resolution system and have the appropriate parameters. We present a nontriangular local resolution system for a difference family BIBD construction of Sprott.

Keywords
BIBD, balanced incomplete block design, combinatorial design, block design, design, difference family, generalized quadrangle, ovoid, spread
Mathematical Subject Classification
Primary: 05B25
Secondary: 05B05
Milestones
Received: 2 January 2023
Revised: 14 June 2023
Accepted: 13 July 2024
Published: 25 July 2024
Authors
Ryan McCulloch
Department of Mathematics and Statistics
Binghamton University
Vestal, NY
United States
© 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).