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Nonhomogeneous parking functions and noncrossing partitions
For each skew shape we define a nonhomogeneous symmetric function,
generalizing a construction of Pak and Postnikov. In two special cases, we show
that the coefficients of this function when expanded in the complete
homogeneous basis are given in terms of the (reduced) type of -divisible
noncrossing partitions. Our work extends Haiman's notion of a parking function
symmetric function.Comment: 11 pages, 3 figure
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