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 a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X appears t-apart in at most one block of A for 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 maximum packing is called the packing number, denoted by P(v, k, 1). The values of the function P(v, 5, 1) are determined here for all v ≥5 with a few possible exceptions. This result is established by means of a result on incomplete perfect Mendelsohn designs which is of interest in its own right.
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Bennett, F.E., Yin, J., Zhang, H. et al. Perfect Mendelsohn Packing Designs with Block Size Five. Designs, Codes and Cryptography 14, 5–22 (1998). https://doi.org/10.1023/A:1008200319697
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DOI: https://doi.org/10.1023/A:1008200319697