An Experimental Mathematics Approach to the Area Statistic of Parking Functions

Yao, Yukun; Zeilberger, Doron

doi:10.1007/s00283-018-9848-9

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2022

2023

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Cited by 2 publications

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“…More recently, Diaconis and Hicks [8] studied the distribution of coordinates, descent pattern, area, and other statistics of random parking functions. Yao and Zeilberger [32] used an experimental mathematics approach combined with some probability to study the area statistic. In [20], Kenyon and Yin explored links between combinatorial and probabilistic aspects of parking functions.…”

Section: Introductionmentioning

confidence: 99%

Cycle structure of random parking functions

Paguyo¹

2022

Preprint

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We initiate the study of the cycle structure of uniformly random parking functions. Using the combinatorics of parking completions, we compute the asymptotic expected value of the number of cycles of any fixed length. We obtain an upper bound on the total variation distance between the joint distribution of cycle counts and independent Poisson random variables using a multivariate version of Stein's method via exchangeable pairs. Under a mild condition, the process of cycle counts converges in distribution to a process of independent Poisson random variables.

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Section: Introductionmentioning

confidence: 99%