Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system $C_{n}$

Details Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system $C_{n}$ Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system $C_{n}$

2003-10-23

arxiv.org/abs/math/0310370v2

Mathematics

Combinatorics

Scientific paper

We establish a Morris type recurrence formula for the root system $C_{n}$.\
Next we introduce cyclage graphs for the corresponding Kashiwara-Nakashima's
tableaux and use them to define a charge statistic. Finally we conjecture that
this charge may be used to compute the Kostka-Foulkes polynomials for type
$C_{n}.$

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