Transitive latin bitrades
نویسندگان
چکیده
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.
منابع مشابه
Latin bitrades derived from groups
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 کاملPartitioning 3-homogeneous latin bitrades
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...
متن کاملTo the theory of q-ary Steiner and other-type trades
We introduce the concept of a clique bitrade, which generalizes several known types of bitrades, including latin bitrades, Steiner T(k−1, k, v) bitrades, extended 1perfect bitrades. For a distance-regular graph, we show a one-to-one correspondence between the clique bitrades that meet the weight-distribution lower bound on the cardinality and the bipartite isometric subgraphs that are distance-...
متن کاملAn 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) ...
متن کاملLatin bitrades, dissections of equilateral triangles and abelian groups
Let T = (T∗, T△) be a spherical latin bitrade. With each a = (a1, a2, a3) ∈ T ∗ associate a set of linear equations Eq (T, a) of the form b1 + b2 = b3, where b = (b1, b2, b3) runs through T ∗ \ {a}. Assume a1 = 0 = a2 and a3 = 1. Then Eq (T, a) has in rational numbers a unique solution bi = b̄i. Suppose that b̄i 6= c̄i for all b, c ∈ T ∗ such that Supported by grant MSM 0021620839 Supported by Edu...
متن کامل