# T

## Tetrahedral Numbers

Integers that can be expressed as a tetrahedral array in 3-space. Another charcterization is as the binomial coefficient C(n,4) (for n > 3 ).

An explicit formula for Tn in terms of n is:

Tn = n(n+1)(n+2)/6

## Thrackle

A graph formed by a collection of curves in the plane, with the property that the curves corresponding to any pair of edges meet in a single point, which is either an endpoint of both edges or a place where the two curves cross. Every planar straight line graph thrackle has at most as many edges as vertices; Conway's thrackle conjecture states that this is true even for curved thrackles.

## Transitive

In general, transitivity is a property of a relation: if whenever a~b and b~c , then a~c , the relation is transitive. Equality is a transitive relation, so is (set-wise) containment.

In group theory, when a group has a permutation action on a set, the action is called transitive if there are group elements whose permutation action is to exchange any given pair of elements of the set. Such an action is called doubly-transitive if any two ordered pairs can be exchanged by the permutation action of some group element, triply-transitive if any two ordered triples can be exchanged, etc.

## Tree

A connected graph having no cycles.

## Triangular Numbers

Integers that can be expressed as triangular arrays of dots. Another charcterization is as the binomial coefficient C(n,4) (for n > 3 ).

An explicit formula for the nth triangular number is:

Tn = n(n+1)/2

## Triangulation

A simplicial complex covering all of a given region in R^d.

## Turan's Theorem

Let t and n be positive integers with t at least equal to 2, and n greater than or equal to t. The maximum number of edges of a graph of order n that doesn't contain a complete subgraph of order t is

where the ni form a partition of n into t-1 parts which are as equal as possible.

Furthermore, the complete (t-1)-partite graph with parts of size n1,n2,...nt-1 is the only graph whose number of edges is equal to the bound above but still doesn't contain a complete subgraph of order t.

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

An On-line Dictionary of Combinatorics