Geodesic
A Generalized Major Index Statistic
Séminaire lotharingien de combinatoire, Tome 60 (2009)

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Inspired by the k-inversion statistic for LLT polynomials, we define a k-inversion number and k-descent set for words. Using these, we define a new statistic on words, called the k-major index, that interpolates between the major index and inversion number. We give a bijective proof that the k-major index is equi-distributed with the major index, generalizing a classical result of Foata and rediscovering a result of Kadell. Inspired by recent work of Haglund and Stevens, we give a partial extension of these definitions and constructions to standard Young tableaux. Finally, we give an application to Macdonald polynomials made possible through connections with LLT polynomials. 

@article{SLC_2009_60_a2,
     author = {Sami H. Assaf},
     title = {A {Generalized} {Major} {Index} {Statistic}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {60},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009_60_a2/}
}
TY  - JOUR
AU  - Sami H. Assaf
TI  - A Generalized Major Index Statistic
JO  - Séminaire lotharingien de combinatoire
PY  - 2009
VL  - 60
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2009_60_a2/
ID  - SLC_2009_60_a2
ER  - 
%0 Journal Article
%A Sami H. Assaf
%T A Generalized Major Index Statistic
%J Séminaire lotharingien de combinatoire
%D 2009
%V 60
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2009_60_a2/
%F SLC_2009_60_a2
Sami H. Assaf. A Generalized Major Index Statistic. Séminaire lotharingien de combinatoire, Tome 60 (2009). http://geodesic.mathdoc.fr/item/SLC_2009_60_a2/