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Séminaire Lotharingien de Combinatoire, B54n (2007), 17 pp.

# Alain Lascoux

# Adding +-1 to the Argument of a Hall-Littlewood Polynomial

**Abstract.**
Shifting by +-1 powers sums: *p*_{i} -> *p*_{i} +- 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.

Received: September 5, 2007.
Accepted: September 15, 2007.
Final Version: September 16, 2007.

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