{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T12:20:28Z","timestamp":1783167628131,"version":"3.54.6"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100019413","name":"Yunnan Provincial Department of Education Science Research Fund Project","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100019413","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007846","name":"Yunnan Provincial Department of Education","doi-asserted-by":"publisher","award":["2026J0603"],"award-info":[{"award-number":["2026J0603"]}],"id":[{"id":"10.13039\/501100007846","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Advances in Applied Mathematics"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.aam.2026.103099","type":"journal-article","created":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T11:08:49Z","timestamp":1778152129000},"page":"103099","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Symmetry of the refined q,t-Catalan polynomials for k\u2192-Dyck paths"],"prefix":"10.1016","volume":"179","author":[{"given":"Menghao","family":"Qu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4366-0124","authenticated-orcid":false,"given":"Yingrui","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.aam.2026.103099_br0010","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.aim.2015.07.012","article-title":"Sweep maps: a continuous family of sorting algorithms","volume":"284","author":"Armstrong","year":"2015","journal-title":"Adv. Math."},{"issue":"7","key":"10.1016\/j.aam.2026.103099_br0020","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1006\/eujc.2001.0527","article-title":"MacMahon's partition analysis: the Omega package","volume":"22","author":"Andrews","year":"2001","journal-title":"Eur. J. Comb."},{"issue":"3","key":"10.1016\/j.aam.2026.103099_br0030","doi-asserted-by":"crossref","first-page":"363","DOI":"10.4310\/MAA.1999.v6.n3.a7","article-title":"Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions","volume":"6","author":"Bergeron","year":"1999","journal-title":"Methods Appl. Anal."},{"key":"10.1016\/j.aam.2026.103099_br0040","author":"Beck"},{"key":"10.1016\/j.aam.2026.103099_br0050","series-title":"The q,t-symmetry of the q,t-Catalan number Ck5(q,t)","author":"Chen","year":"2023"},{"issue":"3","key":"10.1016\/j.aam.2026.103099_br0060","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1090\/jams\/893","article-title":"A proof of the shuffle conjecture","volume":"31","author":"Carlsson","year":"2018","journal-title":"J. Am. Math. Soc."},{"key":"10.1016\/j.aam.2026.103099_br0070","article-title":"Decorated Dyck paths, polyominoes, and the Delta conjecture","volume":"278","author":"D'Adderio","year":"2022","journal-title":"Mem. Am. Math. Soc."},{"issue":"4","key":"10.1016\/j.aam.2026.103099_br0080","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s00220-025-05233-5","article-title":"Shuffle theorems and sandpiles","volume":"406","author":"D'Adderio","year":"2025","journal-title":"Commun. Math. Phys."},{"issue":"3","key":"10.1016\/j.aam.2026.103099_br0090","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/S0012-365X(02)00343-6","article-title":"A proof of the q,t-Catalan positivity conjecture","volume":"256","author":"Garsia","year":"2002","journal-title":"Discrete Math."},{"key":"10.1016\/j.aam.2026.103099_br0100","doi-asserted-by":"crossref","DOI":"10.1016\/j.aam.2020.101998","article-title":"On the sweep map for fuss rational Dyck paths","volume":"116","author":"Garsia","year":"2020","journal-title":"Adv. Appl. Math."},{"key":"10.1016\/j.aam.2026.103099_br0110","article-title":"The q,t-Catalan Numbers and the Space of Diagonal Harmonics with an Appendix on the Combinatorics of Macdonald Polynomials","author":"Haglund","year":"2008"},{"key":"10.1016\/j.aam.2026.103099_br0120","doi-asserted-by":"crossref","DOI":"10.1215\/S0012-7094-04-12621-1","article-title":"A combinatorial formula for the character of the diagonal coinvariants","volume":"126","author":"Haglund","year":"2005","journal-title":"Duke Math. J."},{"issue":"6","key":"10.1016\/j.aam.2026.103099_br0140","doi-asserted-by":"crossref","DOI":"10.1016\/j.disc.2023.113426","article-title":"A symmetry on parking functions via Dyck paths","volume":"346","author":"Li","year":"2023","journal-title":"Discrete Math."},{"key":"10.1016\/j.aam.2026.103099_br0150","doi-asserted-by":"crossref","DOI":"10.37236\/1906","article-title":"Conjectured statistics for the higher q,t-Catalan sequences","author":"Loehr","year":"2005","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.aam.2026.103099_br0160","series-title":"Symmetric Functions and Hall Polynomials","author":"Macdonald","year":"1998"},{"issue":"18","key":"10.1016\/j.aam.2026.103099_br0170","doi-asserted-by":"crossref","first-page":"4123","DOI":"10.1215\/00127094-2021-0011","article-title":"Toric braids and (m,n)-parking functions","volume":"170","author":"Mellit","year":"2021","journal-title":"Duke Math. J."},{"key":"10.1016\/j.aam.2026.103099_br0180","series-title":"The q,t-symmetry of the generalized q,t-Catalan number C\u03bb=(ks,(k\u22121)n\u2212s)(q,t) when n=4","author":"Niu","year":"2022"},{"key":"10.1016\/j.aam.2026.103099_br0130","series-title":"Catalan and Crystal Combinatorics","author":"Pappe","year":"2023"},{"key":"10.1016\/j.aam.2026.103099_br0190","article-title":"An area-depth symmetric q,t-Catalan polynomial","volume":"29","author":"Pappe","year":"2022","journal-title":"Electron. J. Comb."},{"issue":"1","key":"10.1016\/j.aam.2026.103099_br0200","article-title":"On generalized Dyck paths","volume":"18","author":"Rukavicka","year":"2011","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.aam.2026.103099_br0210","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1007\/s00029-018-0408-0","article-title":"Sweeping up zeta","volume":"24","author":"Thomas","year":"2018","journal-title":"Sel. Math."},{"issue":"1","key":"10.1016\/j.aam.2026.103099_br0220","article-title":"A fast algorithm for MacMahon's partition analysis","volume":"11","author":"Xin","year":"2004","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.aam.2026.103099_br0230","doi-asserted-by":"crossref","DOI":"10.37236\/8346","article-title":"On the sweep map for k\u2192-Dyck paths","author":"Xin","year":"2019","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.aam.2026.103099_br0240","doi-asserted-by":"crossref","DOI":"10.1016\/j.aam.2022.102455","article-title":"Dinv, area, and bounce for k\u2192-Dyck paths","volume":"143","author":"Xin","year":"2023","journal-title":"Adv. Appl. Math."},{"issue":"1","key":"10.1016\/j.aam.2026.103099_br0250","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1007\/s10801-024-01374-3","article-title":"The q,t-symmetry of the generalized q,t-Catalan number C(k1,k2,k3)(q,t)","volume":"61","author":"Xin","year":"2025","journal-title":"J. Algebr. Comb."}],"container-title":["Advances in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0196885826000710?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0196885826000710?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T12:00:37Z","timestamp":1783166437000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0196885826000710"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":25,"alternative-id":["S0196885826000710"],"URL":"https:\/\/doi.org\/10.1016\/j.aam.2026.103099","relation":{},"ISSN":["0196-8858"],"issn-type":[{"value":"0196-8858","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Symmetry of the refined q,t-Catalan polynomials for -Dyck paths","name":"articletitle","label":"Article Title"},{"value":"Advances in Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.aam.2026.103099","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"103099"}}