{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:48:02Z","timestamp":1761709682942,"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>We introduce Fu\u00df\u2013Catalan complexes as $d$-dimensional generalisations of triangulations of a convex polygon. These complexes are used to refine Catalan numbers and Fu\u00df\u2013Catalan numbers, by introducing colour statistics for triangulations  and Fu\u00df\u2013Catalan complexes.  Our refinements consist in showing that the number of triangulations, respectively of Fu\u00df\u2013Catalan complexes, with a given colour distribution of its vertices is given by closed product formulae. The crucial ingredient in the proof is the Lagrange\u2013Good inversion  formula.<\/jats:p>","DOI":"10.37236\/639","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:43:43Z","timestamp":1578696223000},"source":"Crossref","is-referenced-by-count":1,"title":["Chromatic Statistics for Triangulations and Fu\u00df&amp;ndash;Catalan Complexes"],"prefix":"10.37236","volume":"18","author":[{"given":"R.","family":"Bacher","sequence":"first","affiliation":[]},{"given":"C.","family":"Krattenthaler","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,7,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p152\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p152\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:07:46Z","timestamp":1579284466000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p152"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/639","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,7,22]]},"article-number":"P152"}}