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The transitive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same transitive closure as R. Thus aR^'b for any elements a and b of X, ...

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...

To translate an object means to perform a translation. A translate of a mathematical object means a shifted (i.e., translated) version of the object. Hence, one can speak of ...

A mathematical relationship transforming a function f(x) to the form f(x+a).

An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...

A permutation group in which the permutations are limited to transpositions.

An ordering of permutations in which each two adjacent permutations differ by the transposition of two elements. For the permutations of {1,2,3} there are two listings which ...

A set of n cells in an n×n square such that no two come from the same row and no two come from the same column. The number of transversals of an n×n square is n! (n ...

A transversal design TD_lambda(k,n) of order n, block size k, and index lambda is a triple (V, G, B) such that 1. V is a set of kn elements, 2. G is a partition of V into k ...