Enumerations of vertices among all rooted ordered trees with levels and degrees
Enumerations of vertices among all rooted ordered trees with levels and degrees
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DOI：
10.1016/j.disc.2017.04.007
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发表时间：
2016-05
期刊：
影响因子：
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通讯作者：
Sen-Peng Eu;Seunghyun Seo;Heesung Shin
中科院分区：
文献类型：
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作者：
Sen-Peng Eu;Seunghyun Seo;Heesung Shin
在本文中，我们列举并给出了固定大小的根序树中以下四个顶点集的双射：（i）在水平n的k度的第一个孩子，（ii）在水平n − 1的k度的非第一个孩子，（iii）在水平n的有k− 1个哥哥的叶子，以及（iv）在水平n − 1的出度k的非叶子。我们的结果统一和推广了文献中的几个先前的作品。
In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size:(i) first-children of degree k at level ℓ,(ii) non-first-children of degree k at level ℓ− 1,(iii) leaves having k− 1 elder siblings at level ℓ, and (iv) non-leaves of outdegree k at level ℓ− 1. Our results unite and generalize several previous works in the literature.