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Shifting by \pm 1 powers sums: p_i \to p_i \pm 1 induces a transformation onsymmetric functions that we detail in the case of Hall-Littlewood polynomials.By iteration, this gives a description of these polynomials in terms of planepartitions, as well as some generating functions. We recover in particular anidentity of Warnaar related to Rogers-Ramanujan identities.

Adding \pm 1 to the argument of an Hall-Littlewood polynomial