منابع مشابه
Novel structures in Stanley sequences
Given a set of integers with no three in arithmetic progression, we construct a Stanley sequence by adding integers greedily so that no arithmetic progression is formed. This paper offers two main contributions to the theory of Stanley sequences. First, we characterize well-structured Stanley sequences as solutions to constraints in modular arithmetic, defining the modular Stanley sequences. Se...
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Let N denote the set of all nonnegative integers. Let k ≥ 3 be an integer and A0 = {a1, . . . , at} (a1 < . . . < at) be a nonnegative set which does not contain an arithmetic progression of length k. We denote A = {a1, a2, . . . } defined by the following greedy algorithm: if l ≥ t and a1, . . . , al have already been defined, then al+1 is the smallest integer a > al such that {a1, . . . , al}...
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A set is said to be 3-free if no three elements form an arithmetic progression. Given a 3-free set A of integers 0 = a0 < a1 < · · · < at, the Stanley sequence S(A) = {an} is defined using the greedy algorithm: For each successive n > t, we pick the smallest possible an so that {a0, a1, . . . , an} is 3-free and increasing. Work by Odlyzko and Stanley indicates that Stanley sequences may be div...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.10.017