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

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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.