{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819729,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a sequence $A$ of given length $n$ contained in $\\mathbb{Z}_p^2$ we study how many distinct subsums $A$ must have when $A$ is not \"wasteful\" by containing too many elements in same subgroup. Martin, Peilloux and Wong have made a conjecture for a sharp lower bound and established it when $n$ is not too large whereas Peng has previously established the conjecture for large $n$. In this note we build on these earlier works and add an elementary argument leading to the conjecture for every $n$.Martin, Peilloux and Wong also made a more general conjecture for sequences in $\\mathbb{Z}_p^m$. Here we show that the special case $n = mp-1$ of this conjecture implies the whole conjecture and that the conjecture is equivalent to a strong version of the additive basis conjecture of Jaeger, Linial, Payan and Tarsi.<\/jats:p>","DOI":"10.37236\/3269","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:22:42Z","timestamp":1578687762000},"source":"Crossref","is-referenced-by-count":2,"title":["On Sumsets of Multisets in $\\mathbb{Z}_p^m$"],"prefix":"10.37236","volume":"20","author":[{"given":"Kaisa","family":"Matom\u00e4ki","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,8,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:13:59Z","timestamp":1579241639000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/3269","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,8,30]]},"article-number":"P30"}}