{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:57Z","timestamp":1753893837201,"version":"3.41.2"},"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>For a hypergraph ${\\cal H} = (V,{\\cal E})$, its $d$\u2013fold symmetric product is defined to be $\\Delta^d {\\cal H} = (V^d,\\{E^d |E \\in {\\cal E}\\})$. We give several upper and lower bounds for the $c$-color discrepancy of such products. In particular, we show that the bound ${\\rm disc}(\\Delta^d {\\cal H},2) \\le {\\rm disc}({\\cal H},2)$ proven for all $d$ in [B. Doerr, A. Srivastav, and P. Wehr, Discrepancy of Cartesian products of arithmetic progressions, Electron. J. Combin. 11(2004), Research Paper 5, 16 pp.]  cannot be extended to more than $c = 2$ colors. In fact, for any $c$ and $d$ such that $c$ does not divide $d!$, there are hypergraphs having arbitrary large discrepancy and ${\\rm disc}(\\Delta^d {\\cal H},c) = \\Omega_d({\\rm disc}({\\cal H},c)^d)$. Apart from constant factors (depending on $c$ and $d$), in these cases the symmetric product behaves no better than the general direct product ${\\cal H}^d$, which satisfies ${\\rm disc}({\\cal H}^d,c) = O_{c,d}({\\rm disc}({\\cal H},c)^d)$.<\/jats:p>","DOI":"10.37236\/1066","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:02:28Z","timestamp":1578718948000},"source":"Crossref","is-referenced-by-count":1,"title":["Discrepancy of Symmetric Products of Hypergraphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Benjamin","family":"Doerr","sequence":"first","affiliation":[]},{"given":"Michael","family":"Gnewuch","sequence":"additional","affiliation":[]},{"given":"Nils","family":"Hebbinghaus","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,4,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:11:26Z","timestamp":1579320686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1066","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,4,24]]},"article-number":"R40"}}