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It is known that \n \n $$\\mathsf D_k(G)=n_1+kn_2-1$$<\/jats:tex-math>\n \n \n \n D<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n =<\/mml:mo>\n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n +<\/mml:mo>\n k<\/mml:mi>\n \n n<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n -<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> if \n \n $$G\\cong C_{n_1}\\oplus C_{n_2}$$<\/jats:tex-math>\n \n \n G<\/mml:mi>\n \u2245<\/mml:mo>\n \n C<\/mml:mi>\n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:msub>\n \u2295<\/mml:mo>\n \n C<\/mml:mi>\n \n n<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is a rank 2 group, where \n \n $$1<n_1\\, | \\,n_2$$<\/jats:tex-math>\n \n \n 1<\/mml:mn>\n <<\/mml:mo>\n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n \n \n |<\/mml:mo>\n \n <\/mml:mrow>\n \n n<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. We investigate the associated inverse problem for rank 2 groups, that is, characterizing the structure of zero-sum sequences of length \n \n $$\\mathsf D_k(G)$$<\/jats:tex-math>\n \n \n \n D<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> that can not be partitioned into \n \n $$k+1$$<\/jats:tex-math>\n \n \n k<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> nontrivial zero-sum subsequences.<\/jats:p>","DOI":"10.1007\/s00493-025-00153-3","type":"journal-article","created":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T06:48:40Z","timestamp":1748242120000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Inverse Problem of the k-th Davenport Constants for Groups of Rank 2"],"prefix":"10.1007","volume":"45","author":[{"given":"Qinghai","family":"Zhong","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,26]]},"reference":[{"key":"153_CR1","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.aam.2011.11.007","volume":"48","author":"SD Adhikari","year":"2012","unstructured":"Adhikari, S.D., Grynkiewicz, D.J., Sun, Z.W.: On weighted zero-sum sequences. 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