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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A combinatorial problem of Shields and Pearcy


Author: Stephen H. Schanuel
Journal: Proc. Amer. Math. Soc. 65 (1977), 185-186
MSC: Primary 05A99
MathSciNet review: 0439652
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Abstract: Pearcy and Shields asked the following question. If $ {x_1}, \ldots ,{x_n}$ are positive real numbers, can one always delete a subset D (possibly empty) such that the following two conditions are satisfied: (1) $ \sum \;1/{x_i} \leqslant n$ (sum over all deleted terms), (2) $ \sum \;{x_i} < 1$ (sum over any interval of consecutive terms disjoint from D)? In this note we show that this is always possible.


References [Enhancements On Off] (What's this?)

  • [1] Allen Shields and Carl Pearcy, Almost commuting matrices (in preparation).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0439652-6
PII: S 0002-9939(1977)0439652-6
Article copyright: © Copyright 1977 American Mathematical Society