A latin bitrade (T , T⊗) is a pair of partial latin squares which defines the difference between two arbitrary latin squares L ⊇ T and L⊗ ⊇ T⊗ of the same order. A 3-homogeneous bitrade (T , T⊗) has… (More)

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… (More)

In this paper we determine a class of critical sets in the abelian 2–group that may be obtained from a greedy algorithm. These new critical sets are all 2–critical (each entry intersects an… (More)

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,… (More)

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… (More)

A multi-latin square of order n and index k is an n×n array of multisets, each of cardinality k, such that each symbol from a fixed set of size n occurs k times in each row and k times in each… (More)

In topological terms, the diencephalon lies between the hypothalamus and the midbrain. It is made up of three segments, prosomere 1 (pretectum), prosomere 2 (thalamus), and prosomere 3 (the… (More)

In this note we introduce the concept of the trade space of a latin square. Computations using Sage and the GAP package Simplicial Ho-mology are presented.