Enumerating solution-free sets in the integers
نویسندگان
چکیده
منابع مشابه
Enumerating solution-free sets in the integers
Given a linear equation L, a set A ⊆ [n] is L-free if A does not contain any ‘non-trivial’ solutions to L. In this paper we consider the following three general questions: (i) What is the size of the largest L-free subset of [n]? (ii) How many L-free subsets of [n] are there? (iii) How many maximal L-free subsets of [n] are there? We completely resolve (i) in the case when L is the equation px ...
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Given a linear equation L, a set A ⊆ [n] is L-free if A does not contain any ‘non-trivial’ solutions to L. We determine the precise size of the largest L-free subset of [n] for several general classes of linear equations L of the form px+ qy = rz for fixed p, q, r ∈ N where p ≥ q ≥ r. Further, for all such linear equations L, we give an upper bound on the number of maximal L-free subsets of [n]...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2016
ISSN: 1571-0653
DOI: 10.1016/j.endm.2016.11.004