컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0127 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | (AL) Algebra (AL) |
| 발표시간(Time) | 20th-C-10:50 -- 11:10 |
| 영문제목 (Title(Eng.)) |
Recursive Koszul flattenings of determinant and permanent tensors |
| 저자(Author(s)) |
Jong In Han2, Jeong-Hoon Ju1, Yeongrak Kim1 Pusan National University1, KAIST2 |
| 초록본문(Abstract) | For a given tensor $T$, its tensor rank $\mathbf{R}(T)$ is defined as the smallest number of decomposable tensors $T_1,...,T_r$ needed to express the tensor as $T=T_1+\cdots+T_r$. It is meaningful to calculate the tensor rank in the sense of complexity. However, it is extremely hard to calculate the tensor rank directly, so ones try to improve upper and lower bounds of it. In this talk, we focus on lower bounds for the tensor rank of the determinant and permanent tensors. We will improve the lower bounds using a method which Hauenstein-Oeding-Ottaviani-Sommese suggested. We call the method recursive Koszul flattening. The improved results will give exact tensor rank of both $det_4$ and $perm_4$, and separate $det_n$ and $perm_n$ by their tensor ranks. |
| 분류기호 (MSC number(s)) |
14N07, 15A15 |
| 키워드(Keyword(s)) | Tensor rank, Koszul flattening, recursive Koszul flattening, determinant, permanent |
| 강연 형태 (Language of Session (Talk)) |
Korean |