A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2008

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 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.
Fichier principal
Vignette du fichier
dmAJ0148.pdf (349.38 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01185141 , version 1 (19-08-2015)



Miguel Méndez, Adolfo Rodríguez. A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.557-570, ⟨10.46298/dmtcs.3607⟩. ⟨hal-01185141⟩


57 View
648 Download



Gmail Facebook Twitter LinkedIn More