Geodesic
Standard Tableaux and Modular Major Index
Séminaire lotharingien de combinatoire, 78B (2017)

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

We provide simple necessary and sufficient conditions for the existence of a standard Young tableau of a given shape and major index r mod n, for all r. Our result generalizes the r=1 case due essentially to Klyachko (1974) and proves a recent conjecture due to Sundaram (2016) for the r=0 case. A byproduct of the proof is an asymptotic equidistribution result for ``almost all'' shapes. The proof uses a representation-theoretic formula involving Ramanujan sums and normalized symmetric group character estimates. Further estimates involving ``opposite'' hook lengths are given which are well-adapted to classifying which partitions λ of n have fλ = nd for fixed d. 

@article{SLC_2017_78B_a49,
     author = {Joshua P. Swanson},
     title = {Standard {Tableaux} and {Modular} {Major} {Index}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a49/}
}
TY  - JOUR
AU  - Joshua P. Swanson
TI  - Standard Tableaux and Modular Major Index
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a49/
ID  - SLC_2017_78B_a49
ER  - 
%0 Journal Article
%A Joshua P. Swanson
%T Standard Tableaux and Modular Major Index
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a49/
%F SLC_2017_78B_a49
Joshua P. Swanson. Standard Tableaux and Modular Major Index. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a49/