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Homogeneous toroidal Latin bitrades

Griggs, Terry and Drapal, Ales (2009). Homogeneous toroidal Latin bitrades. In: 22nd British Combinatorial Conference, 05-10 Jul 2009, St Andrews, Scotland.

URL: http://bcc2009.mcs.st-and.ac.uk/docs/bccpbook/pboo...
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Abstract

Let T be a partial Latin square. Then T is a Latin trade if there exists a partial Latin square T1, called a trade mate of T, with the properties that (i) a cell is filled in T1 if and only if it is filled in T, (ii) no entry occurs in the same cell in T and T1, (iii) in any given row or column, T and T1 contain the same elements. The pair {T, T1} is called a Latin bitrade. A Latin trade T (and T1) is said to be (r, c, e)- homogeneous if each row contains precisely r entries, each column contains precisely c entries, and each entry occurs precisely e times. An (r, c, e)-homogeneous Latin bitrade can be embedded on the torus only for three parameter sets, namely (r, c, e) = (3, 3, 3), (4, 4, 2) or (6, 3, 2). In this talk I will present classifications for all three cases.

Item Type: Conference Item
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22733
Depositing User: Sara Griffin
Date Deposited: 10 Sep 2010 10:08
Last Modified: 11 Dec 2012 10:53
URI: http://oro.open.ac.uk/id/eprint/22733
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