Fixed points of a random restricted growth sequence

Abstract

We call $i$ a fixed point of a given sequence if the value of that sequence at the $i$-th position coincides with $i$. Here, we enumerate fixed points in the class of restricted growth sequences. The counting process is conducted by calculation of generating functions and leveraging a probabilistic sampling method.

Final version. A few typos are fixed and the presentation is improved. arXiv admin note: text overlap with arXiv:1912.05060