{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T05:40:05Z","timestamp":1750484405045,"version":"3.41.0"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2007,9,1]],"date-time":"2007-09-01T00:00:00Z","timestamp":1188604800000},"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":[[2007,9]]},"abstract":"<jats:p>We study the gaps in the sequence of sums of <jats:italic>h<\/jats:italic> pairwise distinct elements of a given sequence <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548306008224_inline1\">\n\t      <jats:alt-text>$\\cal{A}$<\/jats:alt-text>\n\t    <\/jats:inline-graphic> in relation to the gaps in the sequence of sums of <jats:italic>h<\/jats:italic> not necessarily distinct elements of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548306008224_inline1\">\n\t      <jats:alt-text>$\\cal{A}$<\/jats:alt-text>\n\t    <\/jats:inline-graphic>. We present several results on this topic. One of them gives a negative answer to a question by Burr and Erd\u0151s.<\/jats:p>","DOI":"10.1017\/s0963548306008224","type":"journal-article","created":{"date-parts":[[2006,11,3]],"date-time":"2006-11-03T12:34:38Z","timestamp":1162557278000},"page":"747-756","source":"Crossref","is-referenced-by-count":2,"title":["Answer to a Question by Burr and Erd\u0151s on Restricted Addition, and Related Results"],"prefix":"10.1017","volume":"16","author":[{"given":"NORBERT","family":"HEGYV\u00c1RI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FRAN\u00c7OIS","family":"HENNECART","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ALAIN","family":"PLAGNE","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,9,1]]},"reference":[{"key":"S0963548306008224_manual_ref-9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01174162"},{"volume-title":"Sequences","year":"1966","author":"Halberstam","key":"S0963548306008224_manual_ref-4"},{"key":"S0963548306008224_manual_ref-2","unstructured":"[2] Erd\u0151s, P. and Graham, R. L. (1980) Old and New Problems and Results in Combinatorial Number Theory, Vol. 28 of Monographies de L'Enseignement Math\u00e9matique."},{"key":"S0963548306008224_manual_ref-8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02546525"},{"key":"S0963548306008224_manual_ref-10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01181357"},{"key":"S0963548306008224_manual_ref-12","doi-asserted-by":"publisher","DOI":"10.5802\/aif.2064"},{"key":"S0963548306008224_manual_ref-3","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-35.1.85"},{"key":"S0963548306008224_manual_ref-7","doi-asserted-by":"publisher","DOI":"10.2307\/2372681"},{"key":"S0963548306008224_manual_ref-1","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1515\/9783110809794.169","volume-title":"Number Theory","author":"Erd\u0151s","year":"1998"},{"key":"S0963548306008224_manual_ref-5","first-page":"199","article-title":"A proof of two Erd\u0151s' conjectures on restricted addition and further results","volume":"560","author":"Hegyv\u00e1ri","year":"2003","journal-title":"J. Reine Angew. Math."},{"key":"S0963548306008224_manual_ref-6","doi-asserted-by":"publisher","DOI":"10.1007\/s11139-005-0830-8"},{"key":"S0963548306008224_manual_ref-11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3845-2"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548306008224","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T05:06:19Z","timestamp":1750482379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548306008224\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9]]},"references-count":12,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2007,1]]}},"alternative-id":["S0963548306008224"],"URL":"https:\/\/doi.org\/10.1017\/s0963548306008224","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2007,9]]}}}