A generalization of k-Cohen-Macaulay simplicial complexes

作者：Haghighi Hassan^*; Yassemi Siamak; Zaare Nahandi Rahim

来源：Arkiv for Matematik, 2012, 50(2): 279-290.

DOI：10.1007/s11512-010-0136-y

For a positive integer k and a non-negative integer t, a class of simplicial complexes, to be denoted by k-CM (t) , is introduced. This class generalizes two notions for simplicial complexes: being k-Cohen-Macaulay and k-Buchsbaum. In analogy with the Cohen-Macaulay and Buchsbaum complexes, we give some characterizations of CM (t) (=1-CM (t) ) complexes, in terms of vanishing of some homologies of its links, and in terms of vanishing of some relative singular homologies of the geometric realization of the complex and its punctured space. We give a result on the behavior of the CM (t) property under the operation of join of two simplicial complexes. We show that a complex is k-CM (t) if and only if the links of its non-empty faces are k-CM (t-1). We prove that for an integer sa parts per thousand currency signd, the (d-s-1)-skeleton of a (d-1)-dimensional k-CM (t) complex is (k+s)-CM (t) . This result generalizes Hibi%26apos;s result for Cohen-Macaulay complexes and Miyazaki%26apos;s result for Buchsbaum complexes.

• 出版日期2012-10