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Andrew Berget ; Brendon Rhoades - Extending the parking space

dmtcs:2325 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2325
Extending the parking spaceConference paper

Authors: Andrew Berget 1; Brendon Rhoades 2

  • 1 Department of Mathematics [Seattle]
  • 2 Department of Mathematics [Univ California San Diego]

The action of the symmetric group Sn on the set Parkn of parking functions of size n has received a great deal of attention in algebraic combinatorics. We prove that the action of Sn on Parkn extends to an action of Sn+1. More precisely, we construct a graded Sn+1-module Vn such that the restriction of Vn to Sn is isomorphic to Parkn. We describe the Sn-Frobenius characters of the module Vn in all degrees and describe the Sn+1-Frobenius characters of Vn in extreme degrees. We give a bivariate generalization V(,m)n of our module Vn whose representation theory is governed by a bivariate generalization of Dyck paths. A Fuss generalization of our results is a special case of this bivariate generalization.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: parking functions,symmetric group,Dyck paths,representation,matriod,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • EMSW21-VIGRE: Focus on Mathematics; Funder: National Science Foundation; Code: 0636297
  • Combinatorics and Representation Theory; Funder: National Science Foundation; Code: 1068861

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