Partitioning 3-homogeneous latin bitrades
| dc.creator | Hamalainen, Carlo | |
| dc.date | 2007-10-04 | |
| dc.date | 2008-03-08 | |
| dc.date.accessioned | 2026-07-07T09:25:22Z | |
| dc.date.available | 2026-07-07T09:25:22Z | |
| dc.description | A latin bitrade $(T^{\diamond}, T^{\otimes})$ is a pair of partial latin squares which defines the difference between two arbitrary latin squares $L^{\diamond} \supseteq T^{\diamond}$ and $L^{\diamond} \supseteq T^{\otimes}$ of the same order. A 3-homogeneous bitrade $(T^{\diamond}, T^{\otimes})$ has three entries in each row, three entries in each column, and each symbol appears three times in $T^{\diamond}$. Cavenagh (2006) showed that any 3-homogeneous bitrade may be partitioned into three transversals. In this paper we provide an independent proof of Cavenagh's result using geometric methods. In doing so we provide a framework for studying bitrades as tessellations of spherical, euclidean or hyperbolic space. | |
| dc.description | 13 pages, 11 figures, fixed the figures. Geometriae Dedicata, Accepted: 13 February 2008, Published online: 5 March 2008 | |
| dc.identifier | https://arxiv.org/abs/0710.0938 | |
| dc.identifier | http://arxiv.org/abs/0710.0938 | |
| dc.identifier | doi:10.1007/s10711-008-9242-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156381 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B15 | |
| dc.title | Partitioning 3-homogeneous latin bitrades | |
| dc.type | text |