The enumeration of cyclic mutually nearly orthogonal Latin squares


DEMİRKALE F. , Donovan D. M. , Kokkala J. I. , Marbach T. G.

JOURNAL OF COMBINATORIAL DESIGNS, cilt.27, ss.265-276, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 27 Konu: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1002/jcd.21647
  • Dergi Adı: JOURNAL OF COMBINATORIAL DESIGNS
  • Sayfa Sayıları: ss.265-276

Özet

In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum mu such that there exists a set of mu cyclic MNOLS of order n for n <= 18, as well as providing a full enumeration of sets and lists of mu cyclic MNOLS of order n under a variety of equivalences with n <= 18. This resolves in the negative a conjecture that proposed that the maximum mu for which a set of mu cyclic MNOLS of order n exists is left ceiling n/4 right ceiling +1.