The q, t-symmetry of the generalized q, t-Catalan number C(k1,k2,k3)(q,t)
We present two distinct proofs of the q , t -symmetry for the generalized q , t -Catalan number C k → ( q , t ) , where k → = ( k 1 , k 2 , k 3 ) . The first proof is derived through the application of MacMahon’s partition analysis. The second proof is established via a direct bijection.
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| Veröffentlicht in: | Journal of algebraic combinatorics 2025-02, Vol.61 (1), Article 8 |
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| container_title | Journal of algebraic combinatorics |
| container_volume | 61 |
| creator | Xin, Guoce Zhang, Yingrui |
| description | We present two distinct proofs of the
q
,
t
-symmetry for the generalized
q
,
t
-Catalan number
C
k
→
(
q
,
t
)
, where
k
→
=
(
k
1
,
k
2
,
k
3
)
. The first proof is derived through the application of MacMahon’s partition analysis. The second proof is established via a direct bijection. |
| doi_str_mv | 10.1007/s10801-024-01374-3 |
| format | Article |
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q
,
t
-symmetry for the generalized
q
,
t
-Catalan number
C
k
→
(
q
,
t
)
, where
k
→
=
(
k
1
,
k
2
,
k
3
)
. The first proof is derived through the application of MacMahon’s partition analysis. The second proof is established via a direct bijection.</description><identifier>ISSN: 0925-9899</identifier><identifier>EISSN: 1572-9192</identifier><identifier>DOI: 10.1007/s10801-024-01374-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Computer Science ; Convex and Discrete Geometry ; Group Theory and Generalizations ; Lattices ; Mathematics ; Mathematics and Statistics ; Order ; Ordered Algebraic Structures ; Symmetry</subject><ispartof>Journal of algebraic combinatorics, 2025-02, Vol.61 (1), Article 8</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-372c6f58cf6bef1cece1c3688ad331fbc65c8da7fe3608257b7cb22cc7d7abf93</cites><orcidid>0000-0003-4366-0124</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10801-024-01374-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10801-024-01374-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Xin, Guoce</creatorcontrib><creatorcontrib>Zhang, Yingrui</creatorcontrib><title>The q, t-symmetry of the generalized q, t-Catalan number C(k1,k2,k3)(q,t)</title><title>Journal of algebraic combinatorics</title><addtitle>J Algebr Comb</addtitle><description>We present two distinct proofs of the
q
,
t
-symmetry for the generalized
q
,
t
-Catalan number
C
k
→
(
q
,
t
)
, where
k
→
=
(
k
1
,
k
2
,
k
3
)
. The first proof is derived through the application of MacMahon’s partition analysis. The second proof is established via a direct bijection.</description><subject>Combinatorics</subject><subject>Computer Science</subject><subject>Convex and Discrete Geometry</subject><subject>Group Theory and Generalizations</subject><subject>Lattices</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Order</subject><subject>Ordered Algebraic Structures</subject><subject>Symmetry</subject><issn>0925-9899</issn><issn>1572-9192</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2025</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KAzEUhYMoWKsv4GrATQsTvUmaSbKUwT8suKnrkMkktT8z0ybTRX0an8Unc-oU3Lm6cPjOufAhdE3glgCIu0hAAsFAJxgIExPMTtCAcEGxIoqeogEoyrGSSp2jixiXAKAk4QP0OvtwyTb9_mpx3FeVa8M-aXzSdunc1S6Y9eLTlUciN61Zmzqpd1XhQpKPViRd0XTFxqNt2o4v0Zk36-iujneI3h8fZvkznr49veT3U2wpQIuZoDbzXFqfFc4T66wjlmVSmpIx4gubcStLI7xjGUjKRSFsQam1ohSm8IoN0U2_uwnNdudiq5fNLtTdS80ImzCacThQtKdsaGIMzutNWFQm7DUBfZCme2m6k6Z_pWnWlVhfih1cz134m_6n9QMpx279</recordid><startdate>20250201</startdate><enddate>20250201</enddate><creator>Xin, Guoce</creator><creator>Zhang, Yingrui</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-4366-0124</orcidid></search><sort><creationdate>20250201</creationdate><title>The q, t-symmetry of the generalized q, t-Catalan number C(k1,k2,k3)(q,t)</title><author>Xin, Guoce ; Zhang, Yingrui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-372c6f58cf6bef1cece1c3688ad331fbc65c8da7fe3608257b7cb22cc7d7abf93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2025</creationdate><topic>Combinatorics</topic><topic>Computer Science</topic><topic>Convex and Discrete Geometry</topic><topic>Group Theory and Generalizations</topic><topic>Lattices</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Order</topic><topic>Ordered Algebraic Structures</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xin, Guoce</creatorcontrib><creatorcontrib>Zhang, Yingrui</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of algebraic combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xin, Guoce</au><au>Zhang, Yingrui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The q, t-symmetry of the generalized q, t-Catalan number C(k1,k2,k3)(q,t)</atitle><jtitle>Journal of algebraic combinatorics</jtitle><stitle>J Algebr Comb</stitle><date>2025-02-01</date><risdate>2025</risdate><volume>61</volume><issue>1</issue><artnum>8</artnum><issn>0925-9899</issn><eissn>1572-9192</eissn><abstract>We present two distinct proofs of the
q
,
t
-symmetry for the generalized
q
,
t
-Catalan number
C
k
→
(
q
,
t
)
, where
k
→
=
(
k
1
,
k
2
,
k
3
)
. The first proof is derived through the application of MacMahon’s partition analysis. The second proof is established via a direct bijection.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10801-024-01374-3</doi><orcidid>https://orcid.org/0000-0003-4366-0124</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0925-9899 |
| ispartof | Journal of algebraic combinatorics, 2025-02, Vol.61 (1), Article 8 |
| issn | 0925-9899 1572-9192 |
| language | eng |
| recordid | cdi_proquest_journals_3134326509 |
| source | SpringerLink Journals |
| subjects | Combinatorics Computer Science Convex and Discrete Geometry Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Symmetry |
| title | The q, t-symmetry of the generalized q, t-Catalan number C(k1,k2,k3)(q,t) |
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