A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers

Miguel Méndez 1 Adolfo Rodríguez 2
1 IVIC - Departamento de Matematica
2 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]
Abstract : 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.
Keywords : Stirling Bell boson $q$-analog rook numbers dual graded graphs
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Communication dans un congrès
Krattenthaler, Christian and Sagan, Bruce. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), pp.557-570, 2008, DMTCS Proceedings
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Miguel Méndez, Adolfo Rodríguez. A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers. Krattenthaler, Christian and Sagan, Bruce. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), pp.557-570, 2008, DMTCS Proceedings. 〈hal-01185141〉

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