On the Number of B-h-Sets

Author(s)

Dellamonica, Jr., Domingos ^[1] ; Kohayakawa, Yoshiharu ^{[2, 1]} ; Lee, Sang June ^[3] ; Roedl, 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, BR-05508090 Sao Paulo - Brazil

^[3] Duksung Womens Univ, Dept Math, Seoul 132714 - 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: COMBINATORICS PROBABILITY & COMPUTING; v. 25, n. 1, SI, p. 108-129, JAN 2016.
• Web of Science Citations: 5

Abstract

A set A of positive integers is a B-h-set if all sums of the form a(1) + ... + a(h), with a(1), ..., a(h) is an element of A and a(1) <= ... <= a(h), are distinct. We provide asymptotic bounds for the number of B-h-sets of a given cardinality contained in the interval {[}n] = [1, ..., n]. As a consequence of our results, we address a problem of Cameron and Erdos (1990) in the context of B-h-sets. We also use these results to estimate the maximum size of a B-h-set contained in a typical (random) subset of {[}n] with a given cardinality. (AU)

• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Jefferson Antonio Galves
• Support type: 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 type: Research Projects - Thematic Grants