On the enumeration of parking functions by leading terms

Sen-Peng Eu, Tung Shan Fu, Chun Ju Lai

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let x=(x1,...,xn) be a sequence of positive integers. An x-parking function is a sequence (a1,...,an) of positive integers whose non-decreasing rearrangement b1≤⋯≤bn satisfies bi≤x1+⋯+xi. In this paper we give a combinatorial approach to the enumeration of (a,b,...,b) -parking functions by their leading terms, which covers the special cases x=(1,...,1), (a,1,...,1), and (b,...,b). The approach relies on bijections between the x-parking functions and labeled rooted forests. To serve this purpose, we present a simple method for establishing the required bijections. Some bijective results between certain sets of x-parking functions of distinct leading terms are also given.

Original languageEnglish
Pages (from-to)392-406
Number of pages15
JournalAdvances in Applied Mathematics
Volume35
Issue number4
DOIs
Publication statusPublished - 2005 Oct 1

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Parking Functions
Parking
Enumeration
Term
Bijection
Integer
Bijective
Rearrangement
Cover
Distinct

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

On the enumeration of parking functions by leading terms. / Eu, Sen-Peng; Fu, Tung Shan; Lai, Chun Ju.

In: Advances in Applied Mathematics, Vol. 35, No. 4, 01.10.2005, p. 392-406.

Research output: Contribution to journalArticle

Eu, Sen-Peng ; Fu, Tung Shan ; Lai, Chun Ju. / On the enumeration of parking functions by leading terms. In: Advances in Applied Mathematics. 2005 ; Vol. 35, No. 4. pp. 392-406.
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