The Boustrophedon Transform for Descent Polytopes

Ehrenborg, Richard; Happ, Alex

doi:10.1007/s00026-019-00422-1

Cited by 2 publications

(3 citation statements)

References 6 publications

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“…Take α 1 = (2, 1, 2) ∈ PF (3,5), α 2 = (1) ∈ PF(1, 1), and α 3 = (2, 1) ∈ PF(2, 2). Then (2, 7, 2, 9, 10, 1) ∈ MS(3, 5, 1, 2) is a multi-shuffle of the three words (2, 1, 2), (7), and (10,9).…”

Section: Parking Function Multi-shufflementioning

confidence: 99%

“…The case in which the taken spots form a contiguous block starting from the first spot in the linear car park, , was first considered by Yan [20], with an explicit formula given in a follow-up work by Gessel and Seo [11]. The formula was generalized by Ehrenborg and Happ [9] to take into account cars of different sizes. More recently, Adeniran et al [1] unified prior work on parking completions for and computed the number of parking functions where the parking preferences of cars are arbitrarily specified utilizing a pair of operations termed Join and Split.…”

Section: Introductionmentioning

confidence: 99%

“…Hence b = (3, 7, 9, 8, 4, 9, 8, 8, 9). The interval parking function connected with this edge-labeled spanning tree is c = (a, b) = ((3, 1, 7, 4, 1, 2, 5, 3, 1),(3,7,9,8,4,9,8,8,9)).…”

mentioning

confidence: 99%

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Parking functions: interdisciplinary connections

Yin

2023

Adv. Appl. Probab.

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Suppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise takes the next available spot if it exists. If all drivers park successfully, the sequence of choices is called a parking function. Classical parking functions correspond to the case $m=n$ . We investigate various probabilistic properties of a uniform parking function. Through a combinatorial construction termed a parking function multi-shuffle, we give a formula for the law of multiple coordinates in the generic situation $m \lesssim n$ . We further deduce all possible covariances: between two coordinates, between a coordinate and an unattempted spot, and between two unattempted spots. This asymptotic scenario in the generic situation $m \lesssim n$ is in sharp contrast with that of the special situation $m=n$ . A generalization of parking functions called interval parking functions is also studied, in which each driver is willing to park only in a fixed interval of spots. We construct a family of bijections between interval parking functions with n cars and n spots and edge-labeled spanning trees with $n+1$ vertices and a specified root.

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