IF 2.4 3区 物理与天体物理 Q1 Mathematics
Yong Kong
{"title":"Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices.","authors":"Yong Kong","doi":"10.1103/PhysRevE.110.054135","DOIUrl":null,"url":null,"abstract":"<p><p>The problem of counting polymer coverings on rectangular lattices is investigated. In this model, a linear rigid polymer covers k adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites are considered as monomers. We prove that for a given number of polymers (k-mers), the number of arrangements for the polymers on two-dimensional rectangular lattices satisfies simple recurrence relations. These recurrence relations are quite general and apply for arbitrary polymer length (k) and the width of the lattices (n). The well-studied monomer-dimer problem is a special case of the monomer-polymer model when k=2. It is known the enumeration of monomer-dimer configurations in planar lattices is #P complete. The recurrence relations shown here have the potential for hints for the solution of long-standing problems in this class of computational complexity.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"110 5-1","pages":"054135"},"PeriodicalIF":2.4000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.110.054135","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

摘要

本文研究了矩形晶格上聚合物覆盖层的计数问题。在这一模型中,线性刚性聚合物覆盖 k 个相邻的晶格位点,没有两个聚合物占据一个共同的位点。这些未被占据的晶格位点被视为单体。我们证明,对于给定数量的聚合物(k-单体),聚合物在二维矩形晶格上的排列数量满足简单的递推关系。这些递推关系非常普遍,适用于任意聚合物长度(k)和网格宽度(n)。研究得很透彻的单体-二聚体问题是 k=2 时单体-聚合物模型的一个特例。众所周知,平面晶格中单体-二聚体构型的枚举是 #P 完整的。这里展示的递推关系有可能为解决这一类计算复杂性中长期存在的问题提供提示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices.

The problem of counting polymer coverings on rectangular lattices is investigated. In this model, a linear rigid polymer covers k adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites are considered as monomers. We prove that for a given number of polymers (k-mers), the number of arrangements for the polymers on two-dimensional rectangular lattices satisfies simple recurrence relations. These recurrence relations are quite general and apply for arbitrary polymer length (k) and the width of the lattices (n). The well-studied monomer-dimer problem is a special case of the monomer-polymer model when k=2. It is known the enumeration of monomer-dimer configurations in planar lattices is #P complete. The recurrence relations shown here have the potential for hints for the solution of long-standing problems in this class of computational complexity.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信