On reducible and primitive subsets of FP, II

Katalin Gyarmati, A. Sárközy

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Abstract

In Part I of this paper, we introduced and studied the notion of reducibility and primitivity of subsets of Fp: a set A ⊂ Fp is said to be reducible if it can be represented in the form A = B + C with B, C ⊂ Fp, |B|, |C| ≥ 2; if there are no such sets B, C, then A is said to be primitive. Here, we introduce and study a strong form of primitivity and reducibility: a set A ⊂ Fp is said to be k-primitive if changing at most k elements of it we always get a primitive set, and it is said to be k-reducible if it has a representation in the form A = B1 + B2 + ··· + Bk with B1, B2,⋯, Bk ⊂ Fp, |B1|, |B2|,⋯, +Bk| ≥ 2.

Original languageEnglish
Pages (from-to)59-77
Number of pages19
JournalQuarterly Journal of Mathematics
Volume68
Issue number1
DOIs
Publication statusPublished - Jan 1 2017

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ASJC Scopus subject areas

  • Mathematics(all)

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