On Sequentially Cohen-Macaulay Complexes and Posets
Combinatorics
2007-05-23 v1 Commutative Algebra
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.
Cite
@article{arxiv.math/0702788,
title = {On Sequentially Cohen-Macaulay Complexes and Posets},
author = {Anders Björner and Michelle Wachs and Volkmar Welker},
journal= {arXiv preprint arXiv:math/0702788},
year = {2007}
}
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