Inconstancy of finite and infinite sequences

Details Inconstancy of finite and infinite sequences Inconstancy of finite and infinite sequences

2009-10-07

arxiv.org/abs/0910.1173v3

Theoretical Computer Science, 412 (2011) 2268-2281

Mathematics

Differential Geometry

Accepted by Theoretical Computer Science

Scientific paper

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.

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