$q$-Hook formula of Gansner type for a generalized Young diagram
The purpose of this paper is to present the $q$-hook formula of Gansner type for a generalized Young diagram in the sense of D. Peterson and R. A. Proctor. This gives a far-reaching generalization of a hook length formula due to J. S. Frame, G. de B. Robinson, and R. M. Thrall. Furthurmore, we give...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2009-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2684/pdf |
| _version_ | 1827324095430131712 |
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| author | Kento Nakada |
| author_facet | Kento Nakada |
| author_sort | Kento Nakada |
| collection | DOAJ |
| description | The purpose of this paper is to present the $q$-hook formula of Gansner type for a generalized Young diagram in the sense of D. Peterson and R. A. Proctor. This gives a far-reaching generalization of a hook length formula due to J. S. Frame, G. de B. Robinson, and R. M. Thrall. Furthurmore, we give a generalization of P. MacMahon's identity as an application of the $q$-hook formula. |
| first_indexed | 2024-04-25T02:03:17Z |
| format | Article |
| id | doaj.art-c1e237038a554985a0c8c190c7c69f00 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:17Z |
| publishDate | 2009-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-c1e237038a554985a0c8c190c7c69f002024-03-07T14:45:40ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502009-01-01DMTCS Proceedings vol. AK,...Proceedings10.46298/dmtcs.26842684$q$-Hook formula of Gansner type for a generalized Young diagramKento Nakada0Wakkanai Hokusei Gakuen UniversityThe purpose of this paper is to present the $q$-hook formula of Gansner type for a generalized Young diagram in the sense of D. Peterson and R. A. Proctor. This gives a far-reaching generalization of a hook length formula due to J. S. Frame, G. de B. Robinson, and R. M. Thrall. Furthurmore, we give a generalization of P. MacMahon's identity as an application of the $q$-hook formula.https://dmtcs.episciences.org/2684/pdfgeneralized young diagramstrace generating functions$q$-hook formulakac-moody lie algebrap. macmahon's identity[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Kento Nakada $q$-Hook formula of Gansner type for a generalized Young diagram Discrete Mathematics & Theoretical Computer Science generalized young diagrams trace generating functions $q$-hook formula kac-moody lie algebra p. macmahon's identity [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | $q$-Hook formula of Gansner type for a generalized Young diagram |
| title_full | $q$-Hook formula of Gansner type for a generalized Young diagram |
| title_fullStr | $q$-Hook formula of Gansner type for a generalized Young diagram |
| title_full_unstemmed | $q$-Hook formula of Gansner type for a generalized Young diagram |
| title_short | $q$-Hook formula of Gansner type for a generalized Young diagram |
| title_sort | q hook formula of gansner type for a generalized young diagram |
| topic | generalized young diagrams trace generating functions $q$-hook formula kac-moody lie algebra p. macmahon's identity [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2684/pdf |
| work_keys_str_mv | AT kentonakada qhookformulaofgansnertypeforageneralizedyoungdiagram |