Artinian O-sequence of socol degree 6 and type 3

Abstract

Froberg and Laksov의 정리에 근거하여 여차원이 3, 형태가 3, 길이가 7인 334개의 Artinian O-수열을 CoCoA를 이용하여 찾았고 그 중 level이 되지 않는 경우에 대해 연구하였다. Theorem과 Remark를 통해 level이 되지 않는 O-수열을 찾아 각 경우에 해당하는 Table을 만들었다. 또한, 앞의 방법을 통해 제거되지 않은 O-수열 중 level이 되지 않는 특별한 경우를 증명하였다. 그 결과, 334개의 O-수열 중 221개가 level이 되지 않음을 증명하였다. 위의 방법으로는 level 여부를 알 수 없는 O-수열 10개가 남았다.|Based on a theorem Froberg and Laksov in [7], 334 Codimension 3, Type 3, and Length 7 Artinian O-sequences was discovered by CoCoA (see Appendix A). Of them, after that, the case, that is not become a level, was studied. After the O-sequence, is not become a level by Theorem and Remark, was found out, the table, which conforms to each case, was completed. Of the O-sequence that was not rejected by the former method the special case, that is not become a level, was also demonstrated. As a result, it was demonstrated that 221 O-sequences, of 334 O-sequences, is not a level. 10 O-sequences, that can not know whether they are a level or not by the former method, was remained.