{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T11:13:05Z","timestamp":1777547585652,"version":"3.51.4"},"reference-count":0,"publisher":"Wiley","issue":"30","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/100009226","name":"National Security Agency","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>A subset of an abelian semigroup is called an asymptotic basis\nfor the semigroup if every element of the semigroup with at most\nfinitely many exceptions can be represented as the sum of two\ndistinct elements of the basis. The representation function of\nthe basis counts the number of representations of an element of\nthe semigroup as the sum of two distinct elements of the basis.\nSuppose there is given function from the semigroup into the set\nof nonnegative integers together with infinity such that this\nfunction has only finitely many zeros. It is proved that for a large class of countably infinite\n abelian semigroups, there exists a basis whose representation\n function is exactly equal to the given function for every\n element in the semigroup.<\/jats:p>","DOI":"10.1155\/s0161171204306046","type":"journal-article","created":{"date-parts":[[2004,7,20]],"date-time":"2004-07-20T11:34:48Z","timestamp":1090323288000},"page":"1589-1597","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Representation functions of additive bases for abelian semigroups"],"prefix":"10.1155","volume":"2004","author":[{"given":"Melvyn B.","family":"Nathanson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,7,18]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/756964.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204306046","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T20:05:29Z","timestamp":1723061129000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204306046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"30","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204306046"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204306046","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-06-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-07-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}