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根植的二进制未标记的树木的编号
Lily Agranat-Tamir1, Shaili Mathur2, Noah A Rosenberg2
1Department of Biology, Stanford University, Stanford, CA, 94305, USA. lilyat@stanford.edu.
Bulletin of mathematical biology
|March 23, 2024
概括
根深蒂固的二进制树,允许循环称为,被列举. 它们的数量增长速度比标准的二进制树快,单树显示出类似的指数增长.
科学领域:
- 组合学是一种组合学.
- 图形理论 图形理论
- 数学的遗传学数学.
背景情况:
- 扎根的二进制树在组合学中是基本的.
- 韦德伯恩-埃瑟林顿计数提供了树木计数的基础.
- 果将循环引入树木结构中,将标准树木泛化.
研究的目的:
- 要列出根系的二进制未标记的树木与n. 叶子.
- 为了确定与未加树相比,加树的生长速度.
- 为了探索数对树木计数的影响.
主要方法:
- 在Wedderburn-Etherington计数技术的基础上.
- 使用递归分解,考虑连接到胆汁的子树.
- 为生成函数推导一个隐含的表达式.
主要成果:
- 根植的二进制树的数量比非树的数量增长得更快.
- 具有单个的树与非树具有相同的指数增长顺序.
- 对于最大树数的最佳数量是中间的.
结论:
- 扎根的二进制树比标准的二进制树提供了更丰富的组合结构.
- 的存在和数量显著影响着树木的数目和生长速度.
- 这些发现对数学遗传学中的建模有潜在的影响.
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