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A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers
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.
Cited literature [12 references]
https://hal.inria.fr/hal-01185141
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, August 19, 2015 - 11:41:14 AM
Last modification on : Tuesday, October 6, 2020 - 10:56:02 AM
Long-term archiving on: : Friday, November 20, 2015 - 10:27:06 AM
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, August 19, 2015 - 11:41:14 AM
Last modification on : Tuesday, October 6, 2020 - 10:56:02 AM
Long-term archiving on: : Friday, November 20, 2015 - 10:27:06 AM
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