On the enumeration of parking functions by leading numbers

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

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

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
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
Country/TerritoryItaly
CityTaormina
Period2005/06/202005/06/25

ASJC Scopus subject areas

  • Algebra and Number Theory

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