### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### 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.

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

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - On the enumeration of parking functions by leading numbers

AU - Eu, Sen Peng

AU - Fu, Tung Shan

AU - Lai, Chun Ju

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84861156880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861156880&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84861156880

SP - 733

EP - 744

ER -