On the Enumeration of Generalized Parking Functions
نویسنده
چکیده
Let x = (x1, x2, . . . , xn) ∈ Nn . Define a x-parking function to be a sequence (a1, a2, . . . , an) of positive integers whose non-decreasing rearrangement b1 ≤ b2 ≤ · · · ≤ bn satisfies bi ≤ x1+ · · ·+xi. Let Pn(x) denote the number of x-parking functions. We discuss the enumerations of such generalized parking functions. In particular, We give the explicit formulas and present two proofs, one by combinatorial argument, and one by recurrence, for the number of x-parking functions for x = (a, n−m−1 z }| { b, . . . , b, c, m−1 z }| { 0, . . . , 0) and x = (a, n−m−1 z }| { b, . . . , b, m z }| { c, . . . , c).
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