Nonhomogeneous parking functions and noncrossing partitions

Drew Armstrong, Sen-Peng Eu

Published 2008-12-03Version 1

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.