A combinatorial problem of Shields and Pearcy
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- by Stephen H. Schanuel
- Proc. Amer. Math. Soc. 65 (1977), 185-186
- DOI: https://doi.org/10.1090/S0002-9939-1977-0439652-6
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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
- Allen Shields and Carl Pearcy, Almost commuting matrices (in preparation).
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 185-186
- MSC: Primary 05A99
- DOI: https://doi.org/10.1090/S0002-9939-1977-0439652-6
- MathSciNet review: 0439652