On the enumeration of parking functions by leading numbers

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

Research output: Contribution to conferencePaper

Abstract

Let x = (x 1,..., x n) be a sequence of positive integers. An x-parking function is a sequence (a 1,..., a n) of positive integers whose non-decreasing rearrangement b 1 ≤ ⋯ ≤b n satisfies b i ≤ x 1 + ⋯ + x i. 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
Pages733-744
Number of pages12
Publication statusPublished - 2005 Dec 1
Event17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy
Duration: 2005 Jun 202005 Jun 25

Other

Other17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05
CountryItaly
CityTaormina
Period05/6/2005/6/25

Fingerprint

Parking Functions
Enumeration
Bijection
Integer
Bijective
Term
Rearrangement
Cover
Distinct

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Eu, S-P., Fu, T. S., & Lai, C. J. (2005). On the enumeration of parking functions by leading numbers. 733-744. Paper presented at 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05, Taormina, Italy.

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

2005. 733-744 Paper presented at 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05, Taormina, Italy.

Research output: Contribution to conferencePaper

Eu, S-P, Fu, TS & Lai, CJ 2005, 'On the enumeration of parking functions by leading numbers' Paper presented at 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05, Taormina, Italy, 05/6/20 - 05/6/25, pp. 733-744.
Eu S-P, Fu TS, Lai CJ. On the enumeration of parking functions by leading numbers. 2005. Paper presented at 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05, Taormina, Italy.
Eu, Sen-Peng ; Fu, Tung Shan ; Lai, Chun Ju. / On the enumeration of parking functions by leading numbers. Paper presented at 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05, Taormina, Italy.12 p.
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