Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version)
Discrete Mathematics
2008-08-21 v2 Combinatorics
Abstract
The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Ces\`aro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence; the coefficients are obtained through some dilation equations. The proofs are based on elementary linear algebra.
Cite
@article{arxiv.0807.1523,
title = {Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version)},
author = {Philippe Dumas},
journal= {arXiv preprint arXiv:0807.1523},
year = {2008}
}