Folding and coloring problems in mathematics and physics
Folding and coloring problems in mathematics and physics
复制标题
数学和物理中的折叠和着色问题
DOI：
10.1090/s0273-0979-00-00870-3
复制
发表时间：
2000
影响因子：
1.3
通讯作者：
P. Francesco
中科院分区：
文献类型：
--
作者：
P. Francesco
我们回顾了膜和聚合物物理中出现的各种折叠问题。这些是（1）束缚膜的幻影折叠，即二维晶格折叠;（2）流体膜的幻影折叠，即任意属的镶嵌的折叠;（3）聚合物的自避免折叠，即曲折问题。这三个问题都与着色问题有关，并具有一种潜在的可积结构，但形式不同。许多数学结果都是利用这一事实得出的。
We review various folding problems arising in the physics of membranes and polymers. These are (1) the phantom folding of tethered membranes, i.e. the two-dimensional lattice folding; (2) the phantom folding of fluid membranes, i.e. the folding of tessellations of arbitrary genus; (3) the self-avoiding folding of polymers, i.e. the meander problem. All three problems are found to be related to coloring problems and possess one kind of underlying integrable structure, in different guises. Many mathematical results follow from taking advantage of this fact.