Strict unimodality of plucking polynomials of rooted trees

Cheng Zhiyun; Mukherjee Sujoy; Przytycki Jdzef H.; Wang Xiao; Yang Seung Yeop

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Strict unimodality of plucking polynomials of rooted trees

机译：拔除生根树木多项式的严格单位

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摘要

We classify rooted trees which have strictly unimodal plucking polynomials (q-polynomials). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients.

机译：我们对根茎树进行了严格的拔除多项式（Q-多项式）。我们还给出了拔除多项式的梯形形状的标准。我们概括了PAK和PANOVA的结果对Q-Binomial系数的严格单位。

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来源
《Journal of knot theory and its ramifications》 |2018年第7期|共19页
作者
Cheng Zhiyun; Mukherjee Sujoy; Przytycki Jdzef H.; Wang Xiao; Yang Seung Yeop;
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作者单位

Beijing Normal Univ Beijing 100875 Peoples R China;

George Washington Univ Washington DC 20052 USA;

George Washington Univ Washington DC 20052 USA;

George Washington Univ Washington DC 20052 USA;

Univ Denver Denver CO 80208 USA;

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正文语种 eng
中图分类纽结理论;
关键词
Plucking polynomial; strict unimodality; rooted tree; Gaussian polynomial; q-binomial coefficients;

机译：采摘多项式;严格的单变性;扎根树;高斯多项式;Q-二进制系数;

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专利

1. Strict unimodality of plucking polynomials of rooted trees [J] . Cheng Zhiyun, Mukherjee Sujoy, Przytycki Jdzef H., Journal of knot theory and its ramifications . 2018,第7期

机译：拔除生根树木多项式的严格单位
2. Tree Descent Polynomials: Unimodality and Central Limit Theorem [J] . Annals of combinatorics . 2020,第1期

机译：树血统多项式：单值和中央极限定理
3. On trees with real-rooted independence polynomial [J] . Bencs Ferenc Discrete mathematics . 2018,第12期

机译：与真正的独立多项式的树木
4. On Unimodality of Independence Polynomials of Some Well-Covered Trees [C] . Vadim E. Levit, Eugen Mandrescu International conference on discrete mathematics and theoretical computer science . 2003

机译：关于一些覆盖树木独立多项式的单层
5. Unimodal Polynomials and Lattice Walk Enumeration with Experimental Mathematics [D] . Ek, Bryan. 2018

机译：单峰多项式和晶格步长枚举与实验数学
6. Inferring rooted species trees from unrooted gene trees using approximate Bayesian computation [O] . Ayed R. A. Alanzi, James H. Degnan -1

机译：使用近似贝叶斯计算从无根基因树推断有根树种
7. Figure 3: (A) Table 2 modified from Kluge (1994: p. 408); (B) nine characters of the Table 2 from Kluge (1994: p. 408) (A) established as a Hennigian trees; (C) strict consensus of three average consensuses of the score 0.27118 resulted the analysis of the forest (B); (D) most parsimonious tree of the length = 11 (CI = 0.8182, RI = 0.9429) based on the Table 2 from Kluge (1994: p. 408). Tree was a posteriori rooted relatively taxon X. [O] . -1

机译：图3：（a）从Kluge修改的表2（1994：p.408）; （b）从Kluge（1994：第408页）的表2的九个字符（1994年：第408页）（a）建立为Hennigian树; （c）严格共识三个平均协商一致的分数0.27118导致森林分析（b）; （d）基于来自Kluge的表2（1994：第408页）的长度= 11（CI = 0.8182，RI = 0.9429）的大多数扩散树。树是一个被扎根的后索相对分类x。
8. Counting Binary, Rooted Trees Arboreal Numbers of the First and Second Kind. Ii. A Recursive Formula for Counting N-Ary Rooted Trees [R] . Weston, P., Ryan, H. F. 1966

机译：计算第一类和第二类树的二元树，根树数。二。计算N元根树的递推公式

Strict unimodality of plucking polynomials of rooted trees

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