Higher nerves of simplicial complexes
Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 803-813.

We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of the Stanley-Reisner ring k[Δ] as well as the f-vector and h-vector of Δ. We present, as an application, a formula for computing regularity of monomial ideals.

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DOI: 10.5802/alco.64
Classification: 05E40,  05E45,  13C15,  13D03
Keywords: Nerve Complex, depth, k-connectivity, homologies, poset, monomial ideals
Dao, Hailong 1; Doolittle, Joseph 1; Duna, Ken 1; Goeckner, Bennet 2; Holmes, Brent 1; Lyle, Justin 1

1 University of Kansas Department of Mathematics 1460 Jayhawk Blvd Lawrence KS 66045, USA
2 Department of Mathematics University of Washington Seattle, WA 98195-4350, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Dao, Hailong; Doolittle, Joseph; Duna, Ken; Goeckner, Bennet; Holmes, Brent; Lyle, Justin. Higher nerves of simplicial complexes. Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 803-813. doi : 10.5802/alco.64. https://alco.centre-mersenne.org/articles/10.5802/alco.64/

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