{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T08:21:05Z","timestamp":1772439665508,"version":"3.50.1"},"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 article, we investigate bijections on various classes of set partitions of classical types that preserve openers and closers.  On the one hand we present bijections for types $B$ and $C$ that interchange crossings and nestings, which generalize a construction by Kasraoui and Zeng for type $A$. On the other hand we generalize a bijection to type $B$ and $C$ that interchanges the cardinality of a maximal crossing with the cardinality of a maximal nesting, as given by Chen, Deng, Du, Stanley and Yan for type $A$. For type $D$, we were only able to construct a bijection between non-crossing and non-nesting set partitions.  For all classical types we show that the set of openers and the set of closers determine a non-crossing or non-nesting set partition essentially uniquely.<\/jats:p>","DOI":"10.37236\/392","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:10:11Z","timestamp":1578715811000},"source":"Crossref","is-referenced-by-count":7,"title":["Crossings and Nestings in Set Partitions of Classical Types"],"prefix":"10.37236","volume":"17","author":[{"given":"Martin","family":"Rubey","sequence":"first","affiliation":[]},{"given":"Christian","family":"Stump","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,9,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r120\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r120\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:27:36Z","timestamp":1579303656000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/392","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9,1]]},"article-number":"R120"}}