Miguel Méndez ; Adolfo Rodríguez - A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers

dmtcs:3607 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3607
A Combinatorial Model for $q$-Generalized Stirling and Bell NumbersArticle

Authors: Miguel Méndez 1; Adolfo Rodríguez 2

  • 1 Departamento de Matematica
  • 2 Laboratoire 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.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: 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]

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