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Biembeddings of Latin squares obtained from a voltage construction

Grannell, Mike and Knor, Martin (2011). Biembeddings of Latin squares obtained from a voltage construction. Australasian Journal of Combinatorics, 51 pp. 259–270.

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We investigate a voltage construction for face $2$-colourable triangulations by $K_{n,n,n}$ from the viewpoint of the underlying Latin squares. We prove that if the vertices are relabelled so that one of the Latin squares is exactly the Cayley table $C_n$ of the group $\mathbb Z_n$, then the other square can be obtained from $C_n$ by a cyclic permutation of row, column or entry identifiers, and we identify these cyclic permutations. As an application, we improve the previously known lower bound for the number of nonisomorphic triangulations by $K_{n,n,n}$ obtained from the voltage construction in the case when $n$ is a prime number.

Item Type: Journal Article
Copyright Holders: 2011 Combinatorial Mathematics Society of Australasia (Inc.)
ISSN: 1034-4942
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 29671
Depositing User: Mike Grannell
Date Deposited: 06 Oct 2011 08:44
Last Modified: 18 Jan 2016 11:15
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