Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903786 | Journal of Combinatorial Theory, Series A | 2018 | 33 Pages |
Abstract
Let the ensemble of an OA be the set of Latin squares derived by interpreting any three columns of the OA as a Latin square. We demonstrate many restrictions on the number of Latin squares of each parity that the ensemble of an OA(k,n) can contain. These restrictions depend on n(mod4) and give some insight as to why it is harder to build projective planes of order nâ¡2(mod4) than for nâ¢2(mod4). For example, we prove that when nâ¡2(mod4) it is impossible to build an OA(n+1,n) for which all Latin squares in the ensemble are isotopic (equivalent to each other up to permutation of the rows, columns and symbols).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Nevena FrancetiÄ, Sarada Herke, Ian M. Wanless,