{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:47Z","timestamp":1753893827673,"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 $G$ with $\\exp(G)=n$, the arithmetical invariant\u00a0$\\mathsf s_A(G)$ is defined to be the least integer $k$ such that\u00a0any sequence $S$ with length $k$ of elements in $G$\u00a0has a $A$ weighted zero-sum subsequence of length $n$. When $A=\\{1\\}$, it is\u00a0the Erd\u0151s-Ginzburg-Ziv constant\u00a0and is denoted by $\\mathsf s (G)$. For certain class of\u00a0sets $A$, we already have some general\u00a0bounds for these weighted constants corresponding to the cyclic\u00a0group $\\mathbb{Z}_n$, which was given by Griffiths. For odd integer $n$, Adhikari and Mazumdar generalized\u00a0the above mentioned results in the sense that they\u00a0hold for more sets $A$. In the present paper we modify Griffiths' method for even $n$\u00a0and obtain general bound\u00a0for the weighted constants for certain class of weighted sets\u00a0which include sets that were not covered by Griffiths for $n\\equiv 0 \\pmod{4}$.<\/jats:p>","DOI":"10.37236\/6285","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:00:11Z","timestamp":1578686411000},"source":"Crossref","is-referenced-by-count":0,"title":["Modification of Griffiths' Result for Even Integers"],"prefix":"10.37236","volume":"23","author":[{"given":"Eshita","family":"Mazumdar","sequence":"first","affiliation":[]},{"given":"Sneh Bala","family":"Sinha","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,10,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:11:01Z","timestamp":1579237861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,28]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6285","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,10,28]]},"article-number":"P4.18"}}