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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Published in | The American mathematical monthly Vol. 129; no. 10; pp. 913 - 923 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Washington
Taylor & Francis
26.11.2022
Taylor & Francis Ltd |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0002-9890 1930-0972 |
DOI: | 10.1080/00029890.2022.2115770 |