{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:38Z","timestamp":1753893818105,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The $q,t$-Catalan numbers can be defined using rational functions,\u00a0geometry related to Hilbert schemes, symmetric functions, representation\u00a0theory, Dyck paths, partition statistics, or Dyck words.\u00a0After decades of intensive study, it was\u00a0eventually proved that all these definitions are equivalent. In this paper,\u00a0we study the similar situation for higher $q,t$-Catalan numbers, where the equivalence of the algebraic and combinatorial definitions is still conjectural. We compute\u00a0the limits of several versions of the modified higher $q,t$-Catalan numbers and\u00a0show that these limits equal the generating function for integer partitions.\u00a0We also identify certain coefficients of the\u00a0higher $q,t$-Catalan numbers as enumerating suitable integer partitions,\u00a0and we make some conjectures on the homological significance of\u00a0the Bergeron-Garsia nabla operator.<\/jats:p>","DOI":"10.37236\/3201","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:24:28Z","timestamp":1578705868000},"source":"Crossref","is-referenced-by-count":3,"title":["Limits of Modified Higher $q,t$-Catalan Numbers"],"prefix":"10.37236","volume":"20","author":[{"given":"Kyungyong","family":"Lee","sequence":"first","affiliation":[]},{"given":"Li","family":"Li","sequence":"additional","affiliation":[]},{"given":"Nicholas A","family":"Loehr","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,7,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:16:42Z","timestamp":1579259802000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/3201","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,7,19]]},"article-number":"P4"}}