컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0254 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-14) Topology of Manifolds and Knots (SS-14) |
| 발표시간(Time) | 19th-B-13:20 -- 13:40 |
| 영문제목 (Title(Eng.)) |
Signed mosaic graphs and alternating mosaic number of knots |
| 저자(Author(s)) |
Hwa Jeong Lee1 Dongguk University1 |
| 초록본문(Abstract) | Lomonaco and Kauffman introduced knot mosaics in their work on quantum knots. This definition is intended to represent an actual physical quantum system. A {\em knot $n$-mosaic} is an $n\times n$ matrix of 11 kinds of specific mosaic tiles representing a knot or a link. In this paper, we consider the {\em alternating mosaic number} of an alternating knot $K$ which is defined as the smallest integer $n$ for which $K$ is representable as a reduced alternating knot $n$-mosaic. We define a signed mosaic graph and a diagonal grid graph and construct Hamiltonian cycles derived from the diagonal grid graphs. Using the cycles, we completely determine the alternating mosaic number of torus knots of type $(2,q)$ for $q\geq 2$, which grows in an order of $q^{1/2}$. |
| 분류기호 (MSC number(s)) |
57K10 |
| 키워드(Keyword(s)) | Knot mosaic, mosaic number, alternating mosaic number, signed mosaic graph, diagonal grid graph, Hamiltonian cycle |
| 강연 형태 (Language of Session (Talk)) |
Korean |