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...

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.

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