Planar Eulerian triangulations are equivalent to spherical Latin bitrades
نویسندگان
چکیده
منابع مشابه
An enumeration of spherical latin bitrades
A latin bitrade (T , T⊗) is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. A genus may be associated to a latin bitrade by constructing an embedding of the underlying graph in an oriented surface. We report computational enumeration results on the number of spherical (genus 0) ...
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In this note we give two results. First, if a latin bitrade (T , T) is primary, thin, separated, and Aut(T ) acts regularly on T , then (T , T) may be derived from a group-based construction. Second, if a latin bitrade (T , T) has genus 0 then the disjoint mate T is unique and the autotopism group of T ⋄ is equal to the autotopism group of T.
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A latin bitrade (T , T⊗) is a pair of partial latin squares that define the difference between two arbitrary latin squares L ⊇ T and L⊗ ⊇ T⊗ of the same order. A 3-homogeneous bitrade (T , T⊗) has three entries in each row, three entries in each column, and each symbol appears three times in T . Cavenagh [2] showed that any 3-homogeneous bitrade may be partitioned into three transversals. In th...
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A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. In ([9]) it is shown that a latin bitrade may be thought of as three derangements of the same set, whose product is the identity and whose cycles pairwise have at most one point in common. By letting a group act ...
متن کاملLatin trades in groups defined on planar triangulations
For a finite triangulation of the plane with faces properly coloured white and black, let AW be the abelian group constructed by labelling the vertices with commuting indeterminates and adding relations which say that the labels around each white triangle add to the identity. We show that AW has free rank exactly two. Let A∗W be the torsion subgroup of AW , and A ∗ B the corresponding group for...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2008
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2007.04.002