Some properties of well-based sequences. (Russian) Zbl 1249.11038

Valyuzhenich, A. A.

Diskretn. Anal. Issled. Oper. 18, No. 1, 15-19 (2011).

Summary: S. V. Kitaev [J. Integer Seq. 9, No. 2, Article 06.2.2 (2006; Zbl 1101.05049)] stated a problem of finding the number of well-based sequences and of existence of a bijection between these objects and sets associated with the sequence A103580. Well-based sequences define the class of graphs for which independent sets are enlisted by S. V. Kitaev. We obtain the desirable bijection and prove that the number of well-based sequences increases as \(\Theta (2^{n/2})\).

MSC:

11B75	Other combinatorial number theory
05C69	Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)

Keywords:

well-based sequence; sum-free set

Citations:

Zbl 1101.05049