Geodesic
Nonhomogeneous parking functions and noncrossing partitions
The electronic journal of combinatorics, Tome 15 (2008)

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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.
DOI : 10.37236/870
Classification : 05A15, 05E05
Mots-clés : skew shape, nonhomogeneous symmetric function, parking function symmetric function 
Drew Armstrong; Sen-Peng Eu. Nonhomogeneous parking functions and noncrossing partitions. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/870
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     author = {Drew Armstrong and Sen-Peng Eu},
     title = {Nonhomogeneous parking functions and noncrossing partitions},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/870},
     zbl = {1163.05302},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/870/}
}
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