I am interested in functions $f\colon X\to X$ (where $X$ is some countable set) such that for every $x \in X$ there exists a polynomial $P_x$ such that $\#(f^k)^{-1}(x)=P_x(k)$ for all $k \geq 1$.


  • Are there any known structural results about such funcitons?
  • Do you know of some (algebraic?) context in which functions like this arise?

Why I am interested in such self-maps: at the end of this paper (https://arxiv.org/abs/1708.04850, section 20) we find some such $f$ (specifically, one for each simply-laced root system).


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.