{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:27Z","timestamp":1753893867438,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a finite abelian group $G$ written additively, and a non-empty subset $A\\subset [1,\\exp(G)-1]$ the weighted Davenport Constant of $G$\u00a0 with respect to the set $A$, denoted $D_A(G)$, is the least positive integer $k$ for which the following holds: Given an arbitrary sequence $(x_1,\\ldots,x_k)$ with $x_i\\in G$, there exists a non-empty subsequence\u00a0 $(x_{i_1},\\ldots,x_{i_t})$ along with $a_{j}\\in A$ such that $\\sum_{j=1}^t a_jx_{i_j}=0$. In this paper, we pose and study a natural new extremal problem that arises from the study of $D_A(G)$:\u00a0 For an integer $k\\ge 2$, determine $f^{(D)}_G(k):=\\min\\{|A|: D_A(G)\\le k\\}$ (if the problem posed makes sense). It turns out that for $k$ 'not-too-small', this is a well-posed problem and one of the most interesting cases occurs for $G=\\mathbb{Z}_p$, the cyclic group of prime order, for which we obtain near optimal bounds for all $k$ (for sufficiently large primes $p$), and asymptotically tight (up to constants) bounds for $k=2,4$.<\/jats:p>","DOI":"10.37236\/7996","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:59:26Z","timestamp":1578617966000},"source":"Crossref","is-referenced-by-count":1,"title":["The Weighted Davenport Constant of a Group and a Related Extremal Problem"],"prefix":"10.37236","volume":"26","author":[{"given":"Niranjan","family":"Balachandran","sequence":"first","affiliation":[]},{"given":"Eshita","family":"Mazumdar","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,12,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p51\/7982","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p51\/7982","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:00:09Z","timestamp":1579215609000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7996","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,12,20]]},"article-number":"P4.51"}}