Geodesic
Flag-Major Index and Flag-Inversion Number on Colored Words and Wreath Product
Séminaire lotharingien de combinatoire, Tome 62 (2009-2010)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

In [Proc. Amer. Math. Soc. 19 (1968), 236-240], Dominique Foata constructed a map \Phi, called second fundamental transformation, exchanging the integer-valued statistics inversion number "inv" and major index "maj" on words whose letters are integers. Later, Foata and Han introduced the flag-inversion number "finv" and extended \Phi on signed words and permutations, showing that the flag major index "fmaj" and "finv" were equidistributed. In this paper we give an extension of \Phi to l-colored words. Using this extension, we show that the bistatistics (fmaj,desbis) and (finv,pcol) are equidistributed, where "pcol" is the sum of color powers and "desbis" is a new statistic derived from "des". 

@article{SLC_2009-2010_62_a2,
     author = {Hilarion L. M. Faliharimalala and Arthur Randrianarivony},
     title = {Flag-Major {Index} and {Flag-Inversion} {Number} on {Colored} {Words} and {Wreath} {Product}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {62},
     year = {2009-2010},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a2/}
}
TY  - JOUR
AU  - Hilarion L. M. Faliharimalala
AU  - Arthur Randrianarivony
TI  - Flag-Major Index and Flag-Inversion Number on Colored Words and Wreath Product
JO  - Séminaire lotharingien de combinatoire
PY  - 2009-2010
VL  - 62
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a2/
ID  - SLC_2009-2010_62_a2
ER  - 
%0 Journal Article
%A Hilarion L. M. Faliharimalala
%A Arthur Randrianarivony
%T Flag-Major Index and Flag-Inversion Number on Colored Words and Wreath Product
%J Séminaire lotharingien de combinatoire
%D 2009-2010
%V 62
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a2/
%F SLC_2009-2010_62_a2
Hilarion L. M. Faliharimalala; Arthur Randrianarivony. Flag-Major Index and Flag-Inversion Number on Colored Words and Wreath Product. Séminaire lotharingien de combinatoire, Tome 62 (2009-2010). http://geodesic.mathdoc.fr/item/SLC_2009-2010_62_a2/