Nonhomogeneous parking functions and noncrossing partitions

Details Nonhomogeneous parking functions and noncrossing partitions Nonhomogeneous parking functions and noncrossing partitions

2008-12-03

arxiv.org/abs/0812.0733v1

Electron. J. Comb. 15 (1) (2008), #R146

Mathematics

Combinatorics

11 pages, 3 figures

Scientific paper

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 $k$-divisible noncrossing partitions. Our work extends Haiman's notion of a parking function symmetric function.

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