A class of latin squares derived from finite abelian groups
Commentationes Mathematicae Universitatis Carolinae (2014)
- Volume: 55, Issue: 3, page 401-409
- ISSN: 0010-2628
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topEvans, Anthony B.. "A class of latin squares derived from finite abelian groups." Commentationes Mathematicae Universitatis Carolinae 55.3 (2014): 401-409. <http://eudml.org/doc/261868>.
@article{Evans2014,
abstract = {We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.},
author = {Evans, Anthony B.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {latin squares; bachelor squares; monogamous squares; prolongation; Latin square; bachelor square; confirmed bachelor square; monogamous square; prolongation},
language = {eng},
number = {3},
pages = {401-409},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A class of latin squares derived from finite abelian groups},
url = {http://eudml.org/doc/261868},
volume = {55},
year = {2014},
}
TY - JOUR
AU - Evans, Anthony B.
TI - A class of latin squares derived from finite abelian groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 3
SP - 401
EP - 409
AB - We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.
LA - eng
KW - latin squares; bachelor squares; monogamous squares; prolongation; Latin square; bachelor square; confirmed bachelor square; monogamous square; prolongation
UR - http://eudml.org/doc/261868
ER -
References
top- Belyavskaya G.B., Generalized extension of quasigroups, (Russian), Mat. Issled. 5 (1970), 28–48. MR0284533
- Belyavskaya G.B., Contraction of quasigroups. I., (Russian), Bul. Akad. Stiince RSS Moldoven (1970), 6–12. MR0279219
- Belyavskaya G.B., Contraction of quasigroups. II., (Russian), Bul. Akad. Stiince RSS Moldoven (1970), 3–17. MR0284531
- Danziger P., Wanless I.M., Webb B.S., 10.1016/j.jcta.2010.11.011, J. Combin. Theory Ser. A 118 (2011), 796–807. Zbl1232.05033MR2745425DOI10.1016/j.jcta.2010.11.011
- Deriyenko I.I., Dudek W.A., On prolongation of quasigroups, Quasigroups and Related Systems 16 (2008), 187–198. MR2494876
- Evans A.B., 10.1007/s10623-006-8153-3, Des. Codes Crypt. 40 (2006), 121–130. Zbl1180.05022MR2226287DOI10.1007/s10623-006-8153-3
- Paige L.J., 10.1090/S0002-9904-1947-08842-X, Bull. Amer. Math. Soc. 53 (1947), 590–593. Zbl0033.15101MR0020990DOI10.1090/S0002-9904-1947-08842-X
- Wanless I.M., Transversals in latin squares: a survey, Surveys in combinatorics 2011, pp. 403–437, London Math. Soc. Lecture Note Ser., 392, Cambridge Univ. Press, Cambridge, 2011. Zbl1226.05067MR2866738
- Wanless I.M., Webb B.S., 10.1007/s10623-006-8168-9, Des. Codes Cryptogr. 40 (2006), 131–135. Zbl1180.05023MR2226288DOI10.1007/s10623-006-8168-9
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