Geodesic
Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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

In their paper on Wilf-equivalence for singleton classes, Backelin, West, and Xin introduced a transformation $\phi^*$, defined by an iterative process and operating on (all) full rook placements on Ferrers boards. Bousquet-Mélou and Steingrimsson proved the analogue of the main result of Backelin, West, and Xin in the context of involutions, and in so doing they needed to prove that $\phi^*$ commutes with the operation of taking inverses. The proof of this commutation result was long and difficult, and Bousquet-Mélou and Steingrimsson asked if $\phi^*$ might be reformulated in such a way as to make this result obvious. In the present paper we provide such a reformulation of $\phi^*$, by modifying the growth diagram algorithm of Fomin. This also answers a question of Krattenthaler, who noted that a bijection defined by the unmodified Fomin algorithm obviously commutes with inverses, and asked what the connection is between this bijection and $\phi^*$. 
@article{DMTCS_2012_special_263_a4,
     author = {Bloom, Jonathan and Saracino, Dan},
     title = {Modified {Growth} {Diagrams,} {Permutation} {Pivots,} and the {BWX} {Map} $\phi^*$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3018/}
}
TY  - JOUR
AU  - Bloom, Jonathan
AU  - Saracino, Dan
TI  - Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$
JO  - Discrete mathematics & theoretical computer science
PY  - 2012
VL  - DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3018/
DO  - 10.46298/dmtcs.3018
LA  - en
ID  - DMTCS_2012_special_263_a4
ER  - 
%0 Journal Article
%A Bloom, Jonathan
%A Saracino, Dan
%T Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$
%J Discrete mathematics & theoretical computer science
%D 2012
%V DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3018/
%R 10.46298/dmtcs.3018
%G en
%F DMTCS_2012_special_263_a4
Bloom, Jonathan; Saracino, Dan. Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3018. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3018/

Cité par Sources :