MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am looking for a general theorem which would tell me when a formal series solution exists for an equation over a semiring. One may assume that the semiring is equipped with a (formal) derivative. One may further restrict to the case $$A(X) = H(X, A(X))$$ where $A$ is a formal series in $X$ and $H(X,Y)$ is a polynomial.

Motivation: Trying to find a more precise set of conditions for which Joyal's implicit species theorem holds. [For example, one can easily lift the condition $H(0,0)=0$ to $H(0,0)$ is constant].

share|cite|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.