q-Supernomial coefficients: From riggings to ribbons

Details q-Supernomial coefficients: From riggings to ribbons q-Supernomial coefficients: From riggings to ribbons

2001-07-30

arxiv.org/abs/math/0107214v1

MathPhys Odyssey 2001, M. Kashiwara and T. Miwa (eds.), Birkhaeuser Boston, Cambridge, MA, 2002, pp. 437-454

Mathematics

Combinatorics

19 pages, svcon2e.sty file required

Scientific paper

q-Supernomial coefficients are generalizations of the q-binomial coefficients. They can be defined as the coefficients of the Hall-Littlewood symmetric function in a product of the complete symmetric functions or the elementary symmetric functions. Hatayama et al. give explicit expressions for these q-supernomial coefficients. A combinatorial expression as the generating function of ribbon tableaux with (co)spin statistic follows from the work of Lascoux, Leclerc and Thibon. In this paper we interpret the formulas by Hatayama et al. in terms of rigged configurations and provide an explicit statistic preserving bijection between rigged configurations and ribbon tableaux thereby establishing a new direct link between these combinatorial objects.

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