A bijective proof of the Shor recurrence
A bijective proof of the Shor recurrence
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DOI：
10.1016/j.ejc.2017.12.004
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Victor J. W. Guo
中科院分区：
文献类型：
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作者：
Victor J. W. Guo
在计算树的凯莱公式的方法中，肖尔发现了一个关于不当边数的精确递归关系。Chen和作者在曾文的组合解释的基础上给出了Shor递归的一个双射，回答了Shor的一个问题。本文应用Shor公式对根为1，…，r且有给定数目的非正常边的有根树的森林进行计数，给出了Shor递归的一个新的双射证明.
In an approach to the Cayley formula for counting trees, Shor discovered a refined recurrence relation concerning the number of improper edges. Chen and the author gave a bijection for the Shor recurrence based on the combinatorial interpretations of Zeng, answering a question of Shor. In this paper, we present a new bijective proof of the Shor recurrence by applying Shor’s formula for counting forests of rooted trees with roots 1,…, r and with a given number of improper edges.