Some existence and construction results of polygonal designs

• DOI: 10.1016/j.ejc.2007.06.018
• Publication Date: 2007-08-08T11:20:09Z
• Authors: Gargi Bhattacharyya; John Hegeman; Joohyung Kim; Jeff Langford; Sung Y. Song
• Keywords: Computational Theory and Mathematics; 0502 economics and business; 05 social sciences; Geometry and Topology; Theoretical Computer Science

AbstractThis paper revisits the existence and construction problems for polygonal designs (a special class of partially balanced incomplete block designs associated with regular polygons). We present new polygonal designs with various parameter sets by explicit construction. In doing so we employ several construction methods — some conventional and some new. We also establish a link between a class of polygonal designs of block size 3 and the cyclically generated ‘λ-fold triple systems’. Finally, we show that the existence question for a certain class of polygonal designs is equivalent to the existence question for ‘perfect grouping systems’ which we introduce.