TY - JOUR

T1 - On the enumeration of parking functions by leading terms

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 - 2005/10

Y1 - 2005/10

N2 - Let x=(x1,...,xn) be a sequence of positive integers. An x-parking function is a sequence (a1,...,an) of positive integers whose non-decreasing rearrangement b1≤⋯≤bn satisfies bi≤x1+⋯+xi. 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=(x1,...,xn) be a sequence of positive integers. An x-parking function is a sequence (a1,...,an) of positive integers whose non-decreasing rearrangement b1≤⋯≤bn satisfies bi≤x1+⋯+xi. 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=26444461402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444461402&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2005.03.005

DO - 10.1016/j.aam.2005.03.005

M3 - Article

AN - SCOPUS:26444461402

SN - 0196-8858

VL - 35

SP - 392

EP - 406

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 4

ER -