Document Type

Article

Publication Date

1-2010

Abstract

Define the Linus sequence Ln for n ≥ 1 as a 0–1 sequence with L1 = 0, and Ln chosen so as to minimize the length of the longest immediately repeated block Ln−2r+1 Ln−r = Ln−r+1 Ln. Define the Sally sequence Sn as the length r of the longest repeated block that was avoided by the choice of Ln. We prove several results about these sequences, such as exponential decay of the frequency of highly periodic subwords of the Linus sequence, zero entropy of any stationary process obtained as a limit of word frequencies in the Linus sequence and infinite average value of the Sally sequence. In addition we make a number of conjectures about both sequences.

Publication Title

Combinatorics Probability & Computing

Volume

19

Issue

1

First Page

21

Last Page

46

DOI

http://dx.doi.org/10.1017/S0963548309990198

Required Publisher's Statement

Copyright 2010 Cambridge University Press. The original published version of this article may be found at http://dx.doi.org/10.1017/S0963548309990198.

Subjects - Topical (LCSH)

Sequences (Mathematics); Ergodic theory

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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Included in

Mathematics Commons

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