A parking function of length n is a sequence π=(π₁,, πₙ) of positive integers such that if λ₁≤⋯≤ λₙ is the increasing rearrangement of π₁,,πₙ, then λᵢ≤ i for 1≤ i≤ n. In this paper we obtain some exact results on the number of fixed points and cycles of parking functions. Our proofs will be based on generalizations of Pollak's argument. Extensions of our techniques are discussed.
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Rubey et al. (2024) studied this question.
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