Enumerative combinatorics of various lattice models
- 수학전공
- 조회수2168
- 2016-10-07
Enumerative combinatorics of various lattice models
▣ 연 사 : 오승상 교수(고려대)
▣ 일 시 : 2016년 10월 6일(목) 4:30~5:30
▣ 장 소 : 31316호(수학과 전공강의실)
▣ 대 상 : 수학과 학부생 및 대학원생
▣ 다 과 : 4시 15분부터
Abstract
In this talk, we introduce the state matrix recursion algorithm, proceeding with recurrence relations of state matrices, for the enumeration of two-dimensional regular lattice models such as dimers and trimers, independent vertex sets, multiple self-avoiding walks and polygons, and quantum knot mosaics in rectangular regions. These enumerations are deep and difficult combinatorial problems in lattice statistics. This algorithm is demonstrated by an application to the monomer--dimer problem on the square lattice, on providing the partition function with monomer and dimer activities.