Geodesic
Adding +-1 to the Argument of a Hall-Littlewood Polynomial
Séminaire lotharingien de combinatoire, Tome 54 (2006-2007)

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

Shifting by +-1 powers sums: pi -> pi +- 1 induces a transformation on symmetric functions that we detail in the case of Hall-Littlewood polynomials. By iteration, this gives a description of these polynomials in terms of plane partitions, as well as some generating functions. We recover in particular an identity of Warnaar related to Rogers-Ramanujan identities. 

@article{SLC_2006-2007_54_a13,
     author = {Alain Lascoux},
     title = {Adding +-1 to the {Argument} of a {Hall-Littlewood} {Polynomial}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {54},
     year = {2006-2007},
     url = {http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a13/}
}
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Alain Lascoux. Adding +-1 to the Argument of a Hall-Littlewood Polynomial. Séminaire lotharingien de combinatoire, Tome 54 (2006-2007). http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a13/