{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T03:40:39Z","timestamp":1777520439484,"version":"3.51.4"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2015,9,16]],"date-time":"2015-09-16T00:00:00Z","timestamp":1442361600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>A set<jats:italic>A<\/jats:italic>of positive integers is a<jats:italic>B<jats:sub>h<\/jats:sub>-set<\/jats:italic>if all the sums of the form<jats:italic>a<\/jats:italic><jats:sub>1<\/jats:sub>+ .\u00a0.\u00a0. +<jats:italic>a<jats:sub>h<\/jats:sub><\/jats:italic>, with<jats:italic>a<\/jats:italic><jats:sub>1,.\u00a0.\u00a0.,<\/jats:sub><jats:italic>a<jats:sub>h<\/jats:sub><\/jats:italic>\u2208<jats:italic>A<\/jats:italic>and<jats:italic>a<\/jats:italic><jats:sub>1<\/jats:sub>\u2a7d .\u00a0.\u00a0. \u2a7d<jats:italic>a<jats:sub>h<\/jats:sub><\/jats:italic>, are distinct. We provide asymptotic bounds for the number of<jats:italic>B<jats:sub>h<\/jats:sub><\/jats:italic>-sets of a given cardinality contained in the interval [<jats:italic>n<\/jats:italic>] = {1<jats:sub>,.\u00a0.\u00a0.,<\/jats:sub><jats:italic>n<\/jats:italic>}. As a consequence of our results, we address a problem of Cameron and Erd\u0151s (1990) in the context of<jats:italic>B<jats:sub>h<\/jats:sub><\/jats:italic>-sets. We also use these results to estimate the maximum size of a<jats:italic>B<jats:sub>h<\/jats:sub><\/jats:italic>-sets contained in a typical (random) subset of [<jats:italic>n<\/jats:italic>] with a given cardinality.<\/jats:p>","DOI":"10.1017\/s0963548315000206","type":"journal-article","created":{"date-parts":[[2015,9,16]],"date-time":"2015-09-16T08:19:46Z","timestamp":1442391586000},"page":"108-129","source":"Crossref","is-referenced-by-count":8,"title":["On the Number of<i>B<sub>h<\/sub><\/i>-Sets"],"prefix":"10.1017","volume":"25","author":[{"suffix":"Jr","given":"DOMINGOS","family":"DELLAMONICA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YOSHIHARU","family":"KOHAYAKAWA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SANG JUNE","family":"LEE","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VOJT\u011aCH","family":"R\u00d6DL","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"WOJCIECH","family":"SAMOTIJ","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2015,9,16]]},"reference":[{"key":"S0963548315000206_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(69)80024-4"},{"key":"S0963548315000206_ref23","doi-asserted-by":"crossref","unstructured":"Lee S. 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