Clusters of repetition roots

重复根簇

基本信息

批准号：
19K11815
负责人：
Fazekas Szilard
金额：
$ 2.58万
依托单位：
Akita University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2019
资助国家：
日本
起止时间：
2019-04-01 至 2024-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-19K11815/
关键词：
combinatorics on words repetitions squares distinct squares upper bounds square network distinguished positions Repetitions Squares Combinatorics on words Distinct repetitions

项目摘要

In the last year we managed to extend the technique of anchor positions to represent repetitions with exponents higher than 2. Using this, we showed that our cluster size conjecture holds for single chains of repetition roots with arbitrary integer exponent.We also showed that the bounds given for single chains are optimal by a constructive proof yielding sequences of clusters for any combination of cluster sizes allowed within the bounds. These results have been published in DCFS 2022.A big development from last year was the solution of the Fraenkel-Simpson conjecture by Li and Brlek using properties of Rauzy graphs. We tried to extend their arguments to so called extended Rauzy graphs to prove our clusters conjecture in the general case. The paper presenting those results is under work as of now.

In the last year we managed to extend the technique of anchor positions to represent repetitions with exponents higher than 2. Using this, we showed that our cluster size conjecture holds for single chains of repetition roots with arbitrary integer exponent.We also showed that the bounds given for single chains are optimal by a constructive proof yielding sequences of clusters for any combination of cluster sizes allowed within the bounds.这些结果已在DCFS 2022中发表。去年的一大发展是利用rauzy图的属性的Fraenkel-Simpson猜想解决方案。我们试图将他们的论点扩展到所谓的扩展rauzy图，以证明我们的群集在一般情况下的猜想。截至目前，呈现这些结果的论文正在起作用。

项目成果

期刊论文数量（14）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

On Algorithmic Self-Assembly of Squares by Co-Transcriptional Folding

通过共转录折叠进行正方形的算法自组装

DOI：
发表时间：
2022
期刊：
Leibniz International Proceedings in Informatics (LIPIcs)
影响因子：
0
作者：
Fazekas Szilard Zsolt、Kim Hwee、Matsuoka Ryuichi、Seki Shinnosuke;Takeuchi Hinano
通讯作者：
Takeuchi Hinano

Linear Bounds on the Size of Conformations in Greedy Deterministic Oritatami

贪婪确定性 Oritatami 中构象大小的线性界限

DOI：
10.1142/s0129054121410082
发表时间：
2021
期刊：
International Journal of Foundations of Computer Science
影响因子：
0.8
作者：
Fazekas Szilard Zsolt;Kim Hwee;Matsuoka Ryuichi;Morita Reoto;Seki Shinnosuke
通讯作者：
Seki Shinnosuke

The general case of the clusters conjecture

团簇猜想的一般情况