A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers
We describe a combinatorial model for the $q$-analogs of the generalized Stirling numbers in terms of bugs and colonies. Using both algebraic and combinatorial methods, we derive explicit formulas, recursions and generating functions for these $q$-analogs. We give a weight preserving bijective corre...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3607/pdf |
| _version_ | 1827324067884040192 |
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| author | Miguel Méndez Adolfo Rodríguez |
| author_facet | Miguel Méndez Adolfo Rodríguez |
| author_sort | Miguel Méndez |
| collection | DOAJ |
| description | We describe a combinatorial model for the $q$-analogs of the generalized Stirling numbers in terms of bugs and colonies. Using both algebraic and combinatorial methods, we derive explicit formulas, recursions and generating functions for these $q$-analogs. We give a weight preserving bijective correspondence between our combinatorial model and rook placements on Ferrer boards. We outline a direct application of our theory to the theory of dual graded graphs developed by Fomin. Lastly we define a natural $p,q$-analog of these generalized Stirling numbers. |
| first_indexed | 2024-04-25T02:03:56Z |
| format | Article |
| id | doaj.art-5be9915e7f1340858f25a98a04e930a9 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:56Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-5be9915e7f1340858f25a98a04e930a92024-03-07T14:38:06ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01DMTCS Proceedings vol. AJ,...Proceedings10.46298/dmtcs.36073607A Combinatorial Model for $q$-Generalized Stirling and Bell NumbersMiguel Méndez0Adolfo Rodríguez1Departamento de MatematicaLaboratoire de combinatoire et d'informatique mathématique [Montréal]We describe a combinatorial model for the $q$-analogs of the generalized Stirling numbers in terms of bugs and colonies. Using both algebraic and combinatorial methods, we derive explicit formulas, recursions and generating functions for these $q$-analogs. We give a weight preserving bijective correspondence between our combinatorial model and rook placements on Ferrer boards. We outline a direct application of our theory to the theory of dual graded graphs developed by Fomin. Lastly we define a natural $p,q$-analog of these generalized Stirling numbers.https://dmtcs.episciences.org/3607/pdfstirlingbellboson$q$-analogrook numbersdual graded graphs[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Miguel Méndez Adolfo Rodríguez A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers Discrete Mathematics & Theoretical Computer Science stirling bell boson $q$-analog rook numbers dual graded graphs [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers |
| title_full | A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers |
| title_fullStr | A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers |
| title_full_unstemmed | A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers |
| title_short | A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers |
| title_sort | combinatorial model for q generalized stirling and bell numbers |
| topic | stirling bell boson $q$-analog rook numbers dual graded graphs [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/3607/pdf |
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