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.
|出版狀態||已發佈 - 2005|
|事件||17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, 意大利|
持續時間: 2005 六月 20 → 2005 六月 25
|其他||17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05|
|期間||2005/06/20 → 2005/06/25|
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