{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T11:43:56Z","timestamp":1768736636796,"version":"3.49.0"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2015,11,3]],"date-time":"2015-11-03T00:00:00Z","timestamp":1446508800000},"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":[[2016,5]]},"abstract":"<jats:p>Let<jats:italic>G<\/jats:italic>be an additive abelian group, let<jats:italic>n<\/jats:italic>\u2a7e 1 be an integer, let<jats:italic>S<\/jats:italic>be a sequence over<jats:italic>G<\/jats:italic>of length |<jats:italic>S<\/jats:italic>| \u2a7e<jats:italic>n<\/jats:italic>+ 1, and let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548315000255_inline1\"\/><jats:tex-math>${\\mathsf h}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(<jats:italic>S<\/jats:italic>) denote the maximum multiplicity of a term in<jats:italic>S<\/jats:italic>. Let \u03a3<jats:italic><jats:sub>n<\/jats:sub><\/jats:italic>(<jats:italic>S<\/jats:italic>) denote the set consisting of all elements in<jats:italic>G<\/jats:italic>which can be expressed as the sum of terms from a subsequence of<jats:italic>S<\/jats:italic>having length<jats:italic>n<\/jats:italic>. In this paper, we prove that either<jats:italic>ng<\/jats:italic>\u2208 \u03a3<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>(<jats:italic>S<\/jats:italic>) for every term<jats:italic>g<\/jats:italic>in<jats:italic>S<\/jats:italic>whose multiplicity is at least<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548315000255_inline1\"\/><jats:tex-math>${\\mathsf h}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(<jats:italic>S<\/jats:italic>) \u2212 1 or |\u03a3<jats:italic><jats:sub>n<\/jats:sub><\/jats:italic>(<jats:italic>S<\/jats:italic>)| \u2a7e min{<jats:italic>n<\/jats:italic>+ 1, |<jats:italic>S<\/jats:italic>| \u2212<jats:italic>n<\/jats:italic>+ | supp (<jats:italic>S<\/jats:italic>)| \u2212 1}, where |supp(<jats:italic>S<\/jats:italic>)| denotes the number of distinct terms that occur in<jats:italic>S<\/jats:italic>. When<jats:italic>G<\/jats:italic>is finite cyclic and<jats:italic>n<\/jats:italic>= |<jats:italic>G<\/jats:italic>|, this confirms a conjecture of Y. O. Hamidoune from 2003.<\/jats:p>","DOI":"10.1017\/s0963548315000255","type":"journal-article","created":{"date-parts":[[2015,11,3]],"date-time":"2015-11-03T08:43:42Z","timestamp":1446540222000},"page":"419-435","source":"Crossref","is-referenced-by-count":7,"title":["On<i>n<\/i>-Sums in an Abelian Group"],"prefix":"10.1017","volume":"25","author":[{"given":"WEIDONG","family":"GAO","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DAVID J.","family":"GRYNKIEWICZ","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XINGWU","family":"XIA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2015,11,3]]},"reference":[{"key":"S0963548315000255_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2005.11.010"},{"key":"S0963548315000255_ref9","doi-asserted-by":"publisher","DOI":"10.1006\/jnth.1995.1089"},{"key":"S0963548315000255_ref10","doi-asserted-by":"publisher","DOI":"10.1006\/jnth.1996.0067"},{"key":"S0963548315000255_ref2","unstructured":"Bialostocki A. and Lotspeich M. 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