On the enumeration of parking functions by leading numbers

Sen Peng Eu; Tung Shan Fu; Chun Ju Lai

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 conference › Paper › peer-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 language	English
Pages	733-744
Number of pages	12
Publication status	Published - 2005
Externally published	Yes
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
Country/Territory	Italy
City	Taormina
Period	2005/06/20 → 2005/06/25

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "On the enumeration of parking functions by leading numbers",

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.",

author = "Eu, {Sen Peng} and Fu, {Tung Shan} and Lai, {Chun Ju}",

note = "Funding Information: * Corresponding author. E-mail addresses: speu@nuk.edu.tw (S.-P. Eu), tsfu@npic.edu.tw (T.-S. Fu). 1 Partially supported by National Science Council, Taiwan, ROC (NSC 93-2115-M-390-005). 2 Partially supported by National Science Council, Taiwan, ROC (NSC 93-2115-M-251-001).; 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 ; Conference date: 20-06-2005 Through 25-06-2005",

year = "2005",

language = "English",

pages = "733--744",

}

TY - CONF

T1 - On the enumeration of parking functions by leading numbers

AU - Eu, Sen Peng

AU - Fu, Tung Shan

AU - Lai, Chun Ju

N1 - Funding Information: * Corresponding author. E-mail addresses: speu@nuk.edu.tw (S.-P. Eu), tsfu@npic.edu.tw (T.-S. Fu). 1 Partially supported by National Science Council, Taiwan, ROC (NSC 93-2115-M-390-005). 2 Partially supported by National Science Council, Taiwan, ROC (NSC 93-2115-M-251-001).

PY - 2005

Y1 - 2005

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.

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T2 - 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05

Y2 - 20 June 2005 through 25 June 2005

ER -

On the enumeration of parking functions by leading numbers

Abstract

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ASJC Scopus subject areas

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