The number of B-3-sets of a given cardinality

Author(s)

Dellamonica, Jr., Domingos ^[1] ; Kohayakawa, Yoshiharu ^{[1, 2]} ; Lee, Sang June ^[3] ; Rodl, Vojtech ^[1] ; Samotij, Wojciech ^{[4, 5]}

Affiliation

^[1] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 - USA

^[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

^[3] Duksung Womens Univ, Dept Math, Seoul 01369 - South Korea

^[4] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv - Israel

^[5] Univ Cambridge Trinity Coll, Cambridge CB2 1TQ - England

• Document type: Journal article
• Source: JOURNAL OF COMBINATORIAL THEORY SERIES A; v. 142, p. 44-76, AUG 2016.
• Web of Science Citations: 4

Abstract

A set S of integers is a B-3-set if all the sums of the form a(1) a(2)+a(3), with a(1), a(2) and a(3) epsilon S and a(1) <= a(2) <= a(3), are distinct. We obtain asymptotic bounds for the number of B-3-sets of a given cardinality contained in the interval {[}n] = [1,...,n]. We use these results to estimate the maximum size of a B-3-set contained in a typical (random) subset of {[}n] of a given cardinality. These results confirm conjectures recently put forward by the authors {[}On the number of B-h-sets, Combin. Probab. Comput. 25 (2016), no. 1, 108-127]. (C) 2016 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Oswaldo Baffa Filho
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
• Grantee: Carlos Eduardo Ferreira
• Support Opportunities: Research Projects - Thematic Grants