Geodesic
Balanced labellings of affine permutations
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

We study the $\textit{diagrams}$ of affine permutations and their $\textit{balanced}$ labellings. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced decompositions of affine permutations. In fact, we show that the sum of weight monomials of the $\textit{column strict}$ balanced labellings is the affine Stanley symmetric function defined by Lam and we give a simple algorithm to recover reduced words from balanced labellings. Applying this theory, we give a necessary and sufficient condition for a diagram to be an affine permutation diagram. Finally, we conjecture that if two affine permutations are $\textit{diagram equivalent}$ then their affine Stanley symmetric functions coincide. 
@article{DMTCS_2013_special_264_a26,
     author = {Yoo, Hwanchul and Yun, Taedong},
     title = {Balanced labellings of affine permutations},
     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.2342},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2342/}
}
TY  - JOUR
AU  - Yoo, Hwanchul
AU  - Yun, Taedong
TI  - Balanced labellings of affine permutations
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.2342/
DO  - 10.46298/dmtcs.2342
LA  - en
ID  - DMTCS_2013_special_264_a26
ER  - 
%0 Journal Article
%A Yoo, Hwanchul
%A Yun, Taedong
%T Balanced labellings of affine permutations
%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.2342/
%R 10.46298/dmtcs.2342
%G en
%F DMTCS_2013_special_264_a26
Yoo, Hwanchul; Yun, Taedong. Balanced labellings of affine permutations. 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.2342. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2342/

Cité par Sources :