Some existence and construction results of polygonal designs

  • Authors:

  • Gargi Bhattacharyya;John Hegeman;Joohyung Kim;Jeff Langford;Sung Y. Song

  • Affiliations:

  • Department of Mathematics, Iowa State University, Ames, IA 50011, USA;Department of Economics, Stanford University, Stanford, CA 94305, USA;Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA;Department of Mathematics, Washington University, St. Louis, MO 63130, USA;Department of Mathematics, Iowa State University, Ames, IA 50011, USA

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2008

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Abstract

This 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 '@l-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.