Parking functions, valet functions and priority queues

Gilbey, Julian; Kalikow, Louis H.

doi:10.1016/s0012-365x(98)00245-3

Cited by 12 publications

(2 citation statements)

References 20 publications

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“…This recurrence led to a new bijection between these two objects, constructed via induction. Other bijections were also found, for example, by Knuth [7], Moszkowski [12], and Gilbey and Kalikow [6].…”

Section: Introductionsupporting

confidence: 52%

“…They showed how to enumerate some generalized parking functions from results in uniform order statistics and empirical distributions. Gilbey and Kalikow [6] constructed bijections from the set of parking functions to allowable pairs of permutations of a priority queue. Parking functions have also been of interest to statisticians and probabilists.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Parking Functions, Tree Inversions, and Multicolored Graphs

Yan

2001

Advances in Applied Mathematics

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A generalized x-parking function associated to a positive integer vector of the form a b b b is a sequence a 1 a 2 a n of positive integers whose nondecreasing rearrangementThe set of x-parking functions has the same cardinality as the set of sequences of rooted b-forests on n . We construct a bijection between these two sets. We show that the sum enumerator of complements of x-parking functions is identical to the inversion enumerator of sequences of rooted b-forests by generating function analysis. Combinatorial correspondences between the sequences of rooted forests and x-parking functions are also given in terms of depth-first search and breadth-first search on multicolored graphs.  2001 Elsevier Science

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Section: Introductionsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Generalized Parking Functions, Tree Inversions, and Multicolored Graphs

Yan

2001

Advances in Applied Mathematics

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Priority Queue Sorting and Labeled Trees

Hamel

2003

Annals of Combinatorics

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Permuted composition tableaux, 0-Hecke algebra and labeled binary trees

Tewari

Willigenburg

2019

Journal of Combinatorial Theory, Series A

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We introduce a generalization of semistandard composition tableaux called permuted composition tableaux. These tableaux are intimately related to permuted basement semistandard augmented fillings studied by Haglund, Mason and Remmel. Our primary motivation for studying permuted composition tableaux is to enumerate all possible ordered pairs of permutations (σ 1 , σ 2 ) that can be obtained by standardizing the entries in two adjacent columns of an arbitrary composition tableau. We refer to such pairs as compatible pairs. To study compatible pairs in depth, we define a 0-Hecke action on permuted composition tableaux. This action naturally defines an equivalence relation on these tableaux. Certain distinguished representatives of the resulting equivalence classes in the special case of two-columned tableaux are in bijection with compatible pairs. We provide a bijection between two-columned tableaux and labeled binary trees. This bijection maps a quadruple of descent statistics for 2-columned tableaux to left and right ascent-descent statistics on labeled binary trees introduced by Gessel, and we use it to prove that the number of compatible pairs is (n + 1) n−1 . 14 4.2. Bijection between LD n and SPCT((2 n )) 15 4.3. Plane binary trees, unlabeled and labeled 162010 Mathematics Subject Classification. Primary 05E10, 20C08; Secondary 05A05, 05A19, 05C20, 05E05, 05E15.

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Parking functions, valet functions and priority queues

Cited by 12 publications

References 20 publications

Generalized Parking Functions, Tree Inversions, and Multicolored Graphs

Generalized Parking Functions, Tree Inversions, and Multicolored Graphs

Priority Queue Sorting and Labeled Trees

Permuted composition tableaux, 0-Hecke algebra and labeled binary trees

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