Israel Journal of Mathematics

, Volume 169, Issue 1, pp 295-316

First online:

On sequentially Cohen-Macaulay complexes and posets

  • Anders BjörnerAffiliated withDepartment of Mathematics, Royal Institute of Technology Email author 
  • , Michelle WachsAffiliated withDepartment of Mathematics, University of Miami
  • , Volkmar WelkerAffiliated withFachbereich Mathematik und Informatik, Universität Marburg

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The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for posets is given. Finally, in an appendix we outline connections with ring-theory and survey some uses of sequential Cohen-Macaulayness in commutative algebra.