Cohen-Macaulay Lexsegment Complexes in Arbitrary Codimension  

作　　者：Siamak Yassemi Rahim Zaare-Nahandi Siamak Yassemi Rahim Zaare-Nahandi(School of Mathematics, Statistics ＆ Computer Science University of Tehran, Tehran, Ira)

机构地区：[1]School of Mathematics, Statistics & Computer Science University of Tehran, Tehran, Iran

出　　处：《Algebra Colloquium》2017年第3期401-406,共6页代数集刊（英文版）

摘　　要：We characterize pure lexsegment complexes which are Cohen-Macaulay in arbitrary codimension. More precisely, we prove that any lexsegment complex is Cohen- Macaulay if and only if it is pure and its 1-dimensional links are connected, and that a lexsegment flag complex is Cohen-Macaulay if and only if it is pure and connected. We show that any non-Cohen-Macaulay lexsegment complex is a Buchsbaum complex if and only if it is a pure disconnected flag complex. For t≥2, a lexsegment complex is strictly Cohen-Macaulay in codimension t if and only if it is the join of a lexsegment pure discon- nected flag complex with a （t - 2）-dimensional simplex. When the Stanley-Reisner ideal of a pure lexsegment complex is not quadratic, the complex is Cohen-Macaulay if and only if it is Cohen-Macaulay in some codimension. Our results are based on a characterization of Cohen-Macaulay and Buchsbaum lexsegment complexes by Bonanzinga, Sorrenti and Terai.We characterize pure lexsegment complexes which are Cohen-Macaulay in arbitrary codimension. More precisely, we prove that any lexsegment complex is Cohen- Macaulay if and only if it is pure and its 1-dimensional links are connected, and that a lexsegment flag complex is Cohen-Macaulay if and only if it is pure and connected. We show that any non-Cohen-Macaulay lexsegment complex is a Buchsbaum complex if and only if it is a pure disconnected flag complex. For t≥2, a lexsegment complex is strictly Cohen-Macaulay in codimension t if and only if it is the join of a lexsegment pure discon- nected flag complex with a （t - 2）-dimensional simplex. When the Stanley-Reisner ideal of a pure lexsegment complex is not quadratic, the complex is Cohen-Macaulay if and only if it is Cohen-Macaulay in some codimension. Our results are based on a characterization of Cohen-Macaulay and Buchsbaum lexsegment complexes by Bonanzinga, Sorrenti and Terai.

关 键 词：squarefree lexsegment ideal Cohen-Macaulay complex Buchsbaum complex flag complex CMT COMPLEX 

分 类 号：O641.4[理学—物理化学] Q945.11[理学—化学]