Abstract
The goal of this paper is twofold. First, we give an elementary introduction to the usage of spectral sequences in the combinatorial setting. Second we list a number of applications.
In the first group of applications the simplicial complex is the nerve of a poset; we consider general posets and lattices, as well as partition-type posets. Our last application is of a different nature: the \(\mathcal{S}_n \)-quotient of the complex of directed forests is a simplicial complex whose cell structure is defined combinatorially.
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Kozlov, D.N. Spectral Sequences on Combinatorial Simplicial Complexes. Journal of Algebraic Combinatorics 14, 27–48 (2001). https://doi.org/10.1023/A:1011209803008
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DOI: https://doi.org/10.1023/A:1011209803008