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