{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T20:33:00Z","timestamp":1778013180489,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The inverse problem associated to the Davenport constant for some finite abelian group is the problem of determining the structure of all minimal zero-sum sequences of maximal length over this group, and more generally of long minimal zero-sum sequences.  Results on the maximal multiplicity of an element in a long minimal zero-sum sequence for groups with large exponent are obtained.  For groups of the form $C_2^{r-1}\\oplus C_{2n}$ the results are optimal up to an absolute constant.  And, the inverse problem, for sequences of maximal length, is solved completely for groups of the form $C_2^2 \\oplus C_{2n}$. Some applications of this latter result are presented.  In particular, a characterization, via the system of sets of lengths, of the class group of rings of algebraic integers is obtained for certain types of groups, including $C_2^2 \\oplus C_{2n}$ and $C_3 \\oplus C_{3n}$; and the Davenport constants of groups of the form $C_4^2 \\oplus C_{4n}$ and $C_6^2 \\oplus C_{6n}$ are determined.<\/jats:p>","DOI":"10.37236\/520","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:56:28Z","timestamp":1578714988000},"source":"Crossref","is-referenced-by-count":24,"title":["The Inverse Problem Associated to the Davenport Constant for $C_2\\oplus C_2 \\oplus C_{2n}$, and Applications to the Arithmetical Characterization of Class Groups"],"prefix":"10.37236","volume":"18","author":[{"given":"Wolfgang A.","family":"Schmid","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,2,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:17:14Z","timestamp":1579303034000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/520","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,14]]},"article-number":"P33"}}