Permutation Representation of 3 and 4-Homogenous Latin Bitrades

• Autorzy: Lefevre J.G. , Donovan D. , Drápal A.
• Języki publikacji: EN

Abstrakty

EN

Cavenagh, Donovan and Drápal (2005) gave a construction for 3-homogeneous latin bitrades which was proved by Cavenagh (2006) to give every 3-homogeneous latin bitrade. A corollary is that every 3-homogenous latin bitrade may be partitioned into three disjoint transversals. Using a permutation representation for latin bitrades developed by Drápal, we provide a shorter proof of these results, and then give a construction for a family of separated 4-homogeneous latin bitrades.

Słowa kluczowe

EN

latin trade; latin bitrade; homogeneous

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 84, nr 1
• Strony: 99--110
• Opis fizyczny: bibliogr. 6 poz., wykr.

Twórcy

autor

Lefevre J.G.

autor

Donovan D.

autor

Drápal A.

• Centre for Discrete Mathematics and Computing, University of Queensland, St.Lucia 4072, Australia,

Bibliografia

• [1] Nicholas J. Cavenagh, Embedding 3-homogeneous latin trades into abelian 2-groups, Comment. Math. Univ. Carolin., 45 (2004), 194-212.
• [2] Nicholas J. Cavenagh, Diane Donovan and Aleˇs Dr´apal, 4-homogeneous latin trades, Australasian Journal of Combinatorics, 32, (2005), 285-303.
• [3] Nicholas J. Cavenagh, Diane Donovan and Aleˇs Dr´apal, 3-homogeneous latin trades, Discrete Math., 300 (2005), no. 1-3, 57-70.
• [4] Nicholas J. Cavenaugh, A uniqueness result for 3-homogeneous latin bitrades, Comment. Math. Univ. Carolin., 47 (2006), 337-358.
• [5] Alěs Drápal, Geometry of Latin Trades, manuscript circulated at Loops'03, Prague 2003.
• [6] Alěs Drápal, On a planar construction of quasigroups, Czechoslovak Math. J., 41 (1991), 538-548.