### Table of Contents

## Bands

### Definition

A \emph{band} is a semigroup $\mathbf{B}=\langle B,\cdot \rangle $ such that

$\cdot $ is idempotent: $x\cdot x=x$.

##### Morphisms

Let $\mathbf{B}$ and $\mathbf{C}$ be bands. A morphism from $\mathbf{B}$ to $\mathbf{C}$ is a function $h:B\to C$ that is a homomorphism: $h(xy)=h(x)h(y)$

### Examples

### Basic results

### Properties

### Finite members

$\begin{array}{lr}
f(1)= &1

f(2)= &3

f(3)= &10

f(4)= &46

f(5)= &251

f(6)= &1682

f(7)= &13213

\end{array}$

see also finite bands and http://www.research.att.com/projects/OEIS?Anum=A058112