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Forced differences between terms of subsequences of integer sequences

1983
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Proceedings of the American Mathematical Society
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Let a" a2,. ■ ■ be a sequence of integers and let D = {d¡.áj be a fixed finite set of integers. For each positive integer n we investigate the problem of choosing maximal subsequences a¡,... ,a¡ from a,.a" such that \a,^ -a. \ CO for a ¥= ß. An asymptotic form for t, the maximum length of such subsequences, is derived in the special case a, = i. 0. Introduction. We examine the problem of constructing subsequences a¡,... ,a¡ of a finite sequence ax,...,an of integers with the property that the

doi:10.1090/s0002-9939-1983-0702277-1
fatcat:n26n7tzc4vf6rm4s6calrecscm