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arXiv · 0910.1173

Inconstancy of finite and infinite sequences

Jean-Paul Allouche·Laurence Maillard-Teyssier
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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.

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Jean-Paul Allouche, Laurence Maillard-Teyssier. 2009-10-07. Inconstancy of finite and infinite sequences. https://arxiv.org/abs/0910.1173

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