Travel in an Infinite Desert

A caravan traverses an infinite desert studded with oases. It can rest indefinitely at each oasis. Given the sequence of the oases' locations, how does the number of the caravan's itineraries grow with time? We show that the growth is exponential when the oasis sequence is asymptotically l...

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Bibliographic Details
Published inThe American mathematical monthly Vol. 129; no. 10; pp. 913 - 923
Main Authors Geller, William, Misiurewicz, Michał
Format Journal Article
LanguageEnglish
Published Washington Taylor & Francis 26.11.2022
Taylor & Francis Ltd
Subjects
Accuracy
Deserts
Nonlinear equations
Oases
Population
Primary 05A16
Secondary 37B40
Travel
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Summary:A caravan traverses an infinite desert studded with oases. It can rest indefinitely at each oasis. Given the sequence of the oases' locations, how does the number of the caravan's itineraries grow with time? We show that the growth is exponential when the oasis sequence is asymptotically linear, and subexponential when the oasis sequence is superlinear. Moreover, the growth has to be superpolynomial, but can be barely so.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2022.2115770