On the enumeration of parking functions by leading terms

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2005 Oct
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics


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