Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 799-824 |
| Number of pages | 26 |
| Journal | Mathematics of Computation |
| Volume | 85 |
| Issue number | 298 |
| DOIs | |
| Publication status | Published - 2016 |
| Externally published | Yes |
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Enumeration of MOLS of small order. / Egan, J.; Wanless, I.M.
In: Mathematics of Computation, Vol. 85, No. 298, 2016, p. 799-824.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Enumeration of MOLS of small order
AU - Egan, J.
AU - Wanless, I.M.
PY - 2016
Y1 - 2016
N2 - We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For n ≤ 9 we: (1) determine the number of orthogonal mates for each species of Latin square of order n; (2) calculate the proportion of Latin squares of order n that have an orthogonal mate, and the expected number of mates when a square is chosen uniformly at random; (3) classify all sets of MOLS of order n up to various different notions of equivalence. We also provide a triple of Latin squares of order 10 that is the closest to being a set of MOLS so far found. © 2015 American Mathematical Society.
AB - We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For n ≤ 9 we: (1) determine the number of orthogonal mates for each species of Latin square of order n; (2) calculate the proportion of Latin squares of order n that have an orthogonal mate, and the expected number of mates when a square is chosen uniformly at random; (3) classify all sets of MOLS of order n up to various different notions of equivalence. We also provide a triple of Latin squares of order 10 that is the closest to being a set of MOLS so far found. © 2015 American Mathematical Society.
KW - Latin square
KW - MOLS
KW - Orthogonal mate
KW - Plex
KW - Transversal
UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85000742203&doi=10.1090%2fmcom%2f3010&partnerID=40&md5=7f809f2518b4ba7a81547cc1770009fb
U2 - 10.1090/mcom/3010
DO - 10.1090/mcom/3010
M3 - Article
VL - 85
SP - 799
EP - 824
JO - Mathematics of Computation
JF - Mathematics of Computation
SN - 0025-5718
IS - 298
ER -