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: [email protected] (S.-P. Eu), [email protected] (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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M3 - Paper
AN - SCOPUS:84861156880
SP - 733
EP - 744
T2 - 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05
Y2 - 20 June 2005 through 25 June 2005
ER -