Geodesic
On $k$-crossings and $k$-nestings of permutations
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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

We introduce $k$-crossings and $k$-nestings of permutations. We show that the crossing number and the nesting number of permutations have a symmetric joint distribution. As a corollary, the number of $k$-noncrossing permutations is equal to the number of $k$-nonnesting permutations. We also provide some enumerative results for $k$-noncrossing permutations for some values of $k$. 
@article{DMTCS_2010_special_259_a68,
     author = {Burrill, Sophie and Mishna, Marni and Post, Jacob},
     title = {On $k$-crossings and $k$-nestings of permutations},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2873},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2873/}
}
TY  - JOUR
AU  - Burrill, Sophie
AU  - Mishna, Marni
AU  - Post, Jacob
TI  - On $k$-crossings and $k$-nestings of permutations
JO  - Discrete mathematics & theoretical computer science
PY  - 2010
VL  - DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2873/
DO  - 10.46298/dmtcs.2873
LA  - en
ID  - DMTCS_2010_special_259_a68
ER  - 
%0 Journal Article
%A Burrill, Sophie
%A Mishna, Marni
%A Post, Jacob
%T On $k$-crossings and $k$-nestings of permutations
%J Discrete mathematics & theoretical computer science
%D 2010
%V DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2873/
%R 10.46298/dmtcs.2873
%G en
%F DMTCS_2010_special_259_a68
Burrill, Sophie; Mishna, Marni; Post, Jacob. On $k$-crossings and $k$-nestings of permutations. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2873. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2873/

Cité par Sources :