Forced differences between terms of subsequences of integer sequences
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- by Michael Gilpin and Robert Shelton PDF
- Proc. Amer. Math. Soc. 88 (1983), 569-578 Request permission
Abstract:
Let ${a_1},{a_2}, \ldots$ be a sequence of integers and let $D = \left \{ {{d_1}, \ldots ,{d_k}} \right \}$ be a fixed finite set of integers. For each positive integer $n$ we investigate the problem of choosing maximal subsequences ${a_{{i_1}}}, \ldots ,{a_{{i_t}}}$ from ${a_1}, \ldots ,{a_n}$ such that $\left | {{a_{{i_\alpha }}} - {a_{{i_\beta }}}} \right | \notin D$ for $\alpha \ne \beta$. An asymptotic form for $t$, the maximum length of such subsequences, is derived in the special case ${a_i} = i$.References
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Michael Gilpin and Robert Shelton, Problem 1152, Math. Mag. 55 (1982), 237.
- Chung Laung Liu, Elements of discrete mathematics, McGraw-Hill Computer Science Series, McGraw-Hill Book Co., New York-Auckland-Bogotá, 1977. MR 0520385 —, Topics in combinatorial mathematics, Math. Assoc. Amer., Washington, D.C., 1972.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 569-578
- MSC: Primary 10L10
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702277-1
- MathSciNet review: 702277