Geodesic
Irreducible Symmetric Group Characters of Rectangular Shape
Séminaire lotharingien de combinatoire, Tome 50 (2003-2005)

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We give a new formula for the values of the symmetric group characters indexed by a rectangular shape. In the second part, we investigate the nature of the values of symmetric group characters indexed by arbitrary shapes. We show that, after appropriate normalization, these are polynomials in parameters that naturally encode the shapes, and we present a conjecture pertaining to the sign of the coefficients of these polynomials. 

@article{SLC_2003-2005_50_a3,
     author = {Richard P. Stanley},
     title = {Irreducible {Symmetric} {Group} {Characters} of {Rectangular} {Shape}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {50},
     year = {2003-2005},
     url = {http://geodesic.mathdoc.fr/item/SLC_2003-2005_50_a3/}
}
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TI  - Irreducible Symmetric Group Characters of Rectangular Shape
JO  - Séminaire lotharingien de combinatoire
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UR  - http://geodesic.mathdoc.fr/item/SLC_2003-2005_50_a3/
ID  - SLC_2003-2005_50_a3
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%0 Journal Article
%A Richard P. Stanley
%T Irreducible Symmetric Group Characters of Rectangular Shape
%J Séminaire lotharingien de combinatoire
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Richard P. Stanley. Irreducible Symmetric Group Characters of Rectangular Shape. Séminaire lotharingien de combinatoire, Tome 50 (2003-2005). http://geodesic.mathdoc.fr/item/SLC_2003-2005_50_a3/