Nonhomogeneous Parking Functions and Noncrossing Partitions
Copyright policy )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 $k$-divisible noncrossing partitions. Our work extends Haiman's notion of a parking function symmetric function.
- University of Minnesota United States
- University of Minnesota Morris United States
- Armstrong, Drew D United States
- National University of Kaohsiung Taiwan
nonhomogeneous symmetric function, Symmetric functions and generalizations, skew shape, Exact enumeration problems, generating functions, FOS: Mathematics, parking function symmetric function, Mathematics - Combinatorics, 05A15, 05E05, Combinatorics (math.CO)
nonhomogeneous symmetric function, Symmetric functions and generalizations, skew shape, Exact enumeration problems, generating functions, FOS: Mathematics, parking function symmetric function, Mathematics - Combinatorics, 05A15, 05E05, Combinatorics (math.CO)
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