Geodesic
Extending the parking space
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

Voir la notice de l'article provenant de la source Episciences

The action of the symmetric group $S_n$ on the set $\mathrm{Park}_n$ of parking functions of size $n$ has received a great deal of attention in algebraic combinatorics. We prove that the action of $S_n$ on $\mathrm{Park}_n$ extends to an action of $S_{n+1}$. More precisely, we construct a graded $S_{n+1}$-module $V_n$ such that the restriction of $V_n$ to $S_n$ is isomorphic to $\mathrm{Park}_n$. We describe the $S_n$-Frobenius characters of the module $V_n$ in all degrees and describe the $S_{n+1}$-Frobenius characters of $V_n$ in extreme degrees. We give a bivariate generalization $V_n^{(\ell, m)}$ of our module $V_n$ 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. 
@article{DMTCS_2013_special_264_a9,
     author = {Berget, Andrew and Rhoades, Brendon},
     title = {Extending the parking space},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2325},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2325/}
}
TY  - JOUR
AU  - Berget, Andrew
AU  - Rhoades, Brendon
TI  - Extending the parking space
JO  - Discrete mathematics & theoretical computer science
PY  - 2013
VL  - DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2325/
DO  - 10.46298/dmtcs.2325
LA  - en
ID  - DMTCS_2013_special_264_a9
ER  - 
%0 Journal Article
%A Berget, Andrew
%A Rhoades, Brendon
%T Extending the parking space
%J Discrete mathematics & theoretical computer science
%D 2013
%V DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2325/
%R 10.46298/dmtcs.2325
%G en
%F DMTCS_2013_special_264_a9
Berget, Andrew; Rhoades, Brendon. Extending the parking space. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2325. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2325/

Cité par Sources :