Geodesic
Standard Tableaux and Modular Major Index
Séminaire lotharingien de combinatoire, 78B (2017) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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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},
     year = {2017},
     volume = {78B},
     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
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
%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/