{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:35:56Z","timestamp":1761060956964,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We find the number of compositions over finite abelian groups under two types\u00a0of restrictions: (i) each part belongs to a given subset and (ii) small\u00a0runs of consecutive parts must have given properties.\u00a0Waring's problem over finite fields can be converted to type (i) compositions,\u00a0whereas Carlitz and \"locally Mullen\" compositions can be formulated as type (ii) compositions.\u00a0We use the multisection formula to translate the problem from integers to group elements, the transfer matrix method to do exact counting,\u00a0and finally the Perron-Frobenius theorem to derive asymptotics.\u00a0We also exhibit bijections involving certain restricted classes of\u00a0compositions.<\/jats:p>","DOI":"10.37236\/7591","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:33:54Z","timestamp":1578670434000},"source":"Crossref","is-referenced-by-count":3,"title":["Counting Compositions over Finite Abelian Groups"],"prefix":"10.37236","volume":"25","author":[{"given":"Zhicheng","family":"Gao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew","family":"MacFie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,4,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:34:13Z","timestamp":1579235653000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,27]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7591","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,4,27]]},"article-number":"P2.19"}}