Ralf Hemmecke <address@hidden> writes:
| > The definition you gave is it: least fixed point of
| > X |-> 1 + T × X × X
|
| Hmmm, good question. In Aldor-combinat (AC) we deal with combinatorial
| species. They encode actual structures. The corresponding generating
| series G(x) for binary trees given by your X above has to fulfil the
| equation
|
| G(x) = 1 + x * G(x) * G(x) (+)
|
| As a quadratic formula it has at most 2 solutions. And only one of
| those solution is a power series with only non-negative
| coefficients. Since I don't know what it should mean to say "there are
| -5 trees with 3 nodes", it is clear which solution I choose for the
| generating series.
|
| Assuming that I understand a bit of the theory of species, then there
| is only *one* solution to
|
| X = 1 + T * X * X.
|
| We are not yet dealing with "virtual species" which would allow
| negative coefficients in the generating series.
I realize my sentence could be ambiguous: I meant "least fixed point
in the category of continuous partial orders (CPO)."