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A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers
oleh: Miguel Méndez, Adolfo Rodríguez
Format: | Article |
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Diterbitkan: | Discrete Mathematics & Theoretical Computer Science 2008-01-01 |
Deskripsi
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.