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On sequentially Cohen-Macaulay complexes and posets

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Anders Björner

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    Michelle Wachs

  3. Fachbereich Mathematik und Informatik, Universität Marburg, D-350 32, Marburg, Germany

    Volkmar Welker

Authors
  1. Anders Björner
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  2. Michelle Wachs
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  3. Volkmar Welker
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Corresponding author

Correspondence to Anders Björner.

Additional information

Supported in part by National Science Foundation grants DMS 0302310 and DMS 0604562.

Supported by Deutsche Forschungsgemeinschaft (DFG)

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Björner, A., Wachs, M. & Welker, V. On sequentially Cohen-Macaulay complexes and posets. Isr. J. Math. 169, 295–316 (2009). https://doi.org/10.1007/s11856-009-0012-2

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  • DOI: https://doi.org/10.1007/s11856-009-0012-2

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