# B

## Bell Numbers

The Bell number *B*_{n} gives the number of ways of partitioning
a set of size *n* into non-empty subsets.

## Binomial Coefficient

The coefficients on the monomials in the expansion of a power of a binomial.
Combinatorially, these numbers have an interpretation as a "choice counter",
i.e. the binomial coefficient is the number of ways in
which *k* items can be chosen from amongst a set of *n* items.

The binomial coefficients form the rows of
Pascal's triangle .

## Binomial Theorem

Let *n* be a positive integer. Then for all *x* and
*y*,

where the sum is taken from *k=0* to *k=n*, and
is a binomial coefficient
.

## Bipartite Graph

A graph in which the set of vertices can be
broken into two subsets such that there are no edges between vertices in
the same subset. This concept extends naturally up to n-partite graphs.

## Bridge

A bridge in a connected graph is an edge whose
removal would disconnect the graph. Edges which are bridges are also sometimes
known as isthmuses. An easy example: in a tree, every edge
is a bridge.

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An On-line Dictionary of Combinatorics