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Integral ordered monoids
Abbreviation: IOMon
Definition
An \emph{integral ordered monoid} is a ordered monoid A=⟨A,⋅,1,≤⟩ that is
\emph{integral}: x≤1
Morphisms
Let A and B be ordered monoids. A morphism from A to B is a function h:A→B that is a orderpreserving homomorphism: h(x⋅y)=h(x)⋅h(y), h(1)=1, x≤y⟹h(x)≤h(y).
Examples
Example 1:
Basic results
Properties
Finite members
f(n)= number of members of size n.
f(1)=1f(2)=1f(3)=2f(4)=8f(5)=44f(6)=308f(7)=2641f(8)=27120f(9)=