Abbreviation: SepAlg
A \emph{separation algebra} is a generalized separation algebra such that
⋅ is \emph{commutative}: x⋅y=y⋅x.
I.e., a separation algebra is a cancellative commutative partial monoid.
Let A and B be cancellative partial monoids. A morphism from A to B is a function h:A→B that is a homomorphism: h(e)=e and if x⋅y≠∗ then h(x⋅y)=h(x)⋅h(y).
Example 1:
$\begin{array}{lr}
f(1)= &1\\ f(2)= &2\\ f(3)= &3\\ f(4)= &8\\ f(5)= &13\\ f(6)= &39\\ f(7)= &120\\ f(8)= &507\\ f(9)= &\\ f(10)= &\\
\end{array}$