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Grannell, Mike and Knor, Martin
(2011).
URL: http://ajc.maths.uq.edu.au/?page=get_volumes&volum...
Abstract
We investigate a voltage construction for face -colourable triangulations by
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
of the group
, then the other square can be obtained from
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
obtained from the voltage construction in the case when
is a prime number.