Inconstancy of finite and infinite sequences
Differential Geometry
2012-02-02 v3 Dynamical Systems
Abstract
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we introduce the inconstancy of a sequence and we show why it seems more pertinent than other criteria for measuring its variational complexity. We also compute the inconstancy of classical binary sequences including some automatic sequences and Sturmian sequences.
Keywords
Cite
@article{arxiv.0910.1173,
title = {Inconstancy of finite and infinite sequences},
author = {Jean-Paul Allouche and Laurence Maillard-Teyssier},
journal= {arXiv preprint arXiv:0910.1173},
year = {2012}
}
Comments
Accepted by Theoretical Computer Science