{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:25Z","timestamp":1759335925854,"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>This note contains two results on the distribution of $k$-crossings and $k$-nestings in graphs. On the positive side, we exhibit a class of graphs for which there are as many $k$-noncrossing $2$-nonnesting graphs as $k$-nonnesting $2$-noncrossing graphs. This class consists of the graphs on $[n]$ where each vertex $x$ is joined to at most one vertex $y$ with $y &lt; x$. On the negative side, we show that this is not the case if we consider arbitrary graphs. The counterexample is given in terms of fillings of Ferrers diagrams and solves a problem of Krattenthaler.<\/jats:p>","DOI":"10.37236\/1159","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:55:20Z","timestamp":1578718520000},"source":"Crossref","is-referenced-by-count":8,"title":["On the Symmetry of the Distribution of $k$-Crossings and $k$-Nestings in Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Anna","family":"De Mier","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,11,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:05:46Z","timestamp":1579320346000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1n21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,11,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1159","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,11,23]]},"article-number":"N21"}}