### 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 language | English |
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Pages | 733-744 |

Number of pages | 12 |

Publication status | Published - 2005 Dec 1 |

Event | 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy Duration: 2005 Jun 20 → 2005 Jun 25 |

### Other

Other | 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 |
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Country | Italy |

City | Taormina |

Period | 05/6/20 → 05/6/25 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*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.