Generalized Gončarov polynomials associated to a delta operator and interpolation grid are realized as weight enumerators in partition lattices and enumerate enriched structures of vector parking functions in exponential families.
Levinson, The Gontcharoff polynomials , Duke Math
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Gon\v{c}arov Polynomials in Partition Lattices and Exponential Families
Generalized Gončarov polynomials associated to a delta operator and interpolation grid are realized as weight enumerators in partition lattices and enumerate enriched structures of vector parking functions in exponential families.