{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:23Z","timestamp":1753893803546,"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>In this paper, we establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type $\\sum_{\\pi\\in {\\Bbb P}(U)} (-1)^{|\\pi|-1} (|\\pi|-1)! f(\\pi)$ where $U$ is a finite set, ${\\Bbb P}(U)$ is the partition lattice of $U$ and $f:{\\Bbb P}(U)\\rightarrow{\\Bbb R}$ is some suitable non-negative function.  Applications of this new analogue are given to counting connected $k$-uniform hypergraphs, network reliability, and cumulants.<\/jats:p>","DOI":"10.37236\/1838","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:31:06Z","timestamp":1578709866000},"source":"Crossref","is-referenced-by-count":2,"title":["Bonferroni-Galambos Inequalities for Partition Lattices"],"prefix":"10.37236","volume":"11","author":[{"given":"Klaus","family":"Dohmen","sequence":"first","affiliation":[]},{"given":"Peter","family":"Tittmann","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,11,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r85\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r85\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:52:36Z","timestamp":1579323156000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r85"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1838","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,11,30]]},"article-number":"R85"}}