Perfect Mendelsohn Packing Designs with Block Size Five

Authors:
F. E. Bennett;J. Yin;H. Zhang;R. J. R. Abel
Affiliations:
Department of Mathematics, Mount Saint Vincent University, Halifax, Nova Scotia, Canada B3M 2J6;Department of Mathematics, Suzhou University, Suzhou, 215006, P. R. China;Department of Computer Science, University of Iowa, Iowa City, IA 52240, USA;School of Mathematics, University of New South Wales, Kensington, NSW 2033, Australia
Venue:
Designs, Codes and Cryptography
Year:
1998

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Abstract

A (v, k, 1) perfect Mendelsohn packing design (briefly (v, k,1)-PMPD) is a pair (X, A) where X is a v-set (of points) and A is acollection of cyclically ordered k-subsets of X (called blocks) such thatevery ordered pair of points of X appears t-apart in at most one block of Afor all t = 1, 2, …, k-1. If no other such packing has more blocks,the packing is said to be maximum and the number of blocks in a maximumpacking is called the packing number, denoted by P(v, k, 1). The values ofthe function P(v, 5, 1) are determined here for all v ≥5 with a fewpossible exceptions. This result is established by means of a result onincomplete perfect Mendelsohn designs which is of interest in its ownright.