no. 5
Higher nerves of simplicial complexes
Dao, Hailong1 ; Doolittle, Joseph1 ; Duna, Ken1 ; Goeckner, Bennet2 ; Holmes, Brent1 ; Lyle, Justin1
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
Algebraic Combinatorics, Tome 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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Révisé le :
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DOI : 10.5802/alco.64
Classification : 05E40, 05E45, 13C15, 13D03
Mots clés : 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 
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Dao, Hailong; Doolittle, Joseph; Duna, Ken; Goeckner, Bennet; Holmes, Brent; Lyle, Justin. Higher nerves of simplicial complexes. Algebraic Combinatorics, Tome 2 (2019) no. 5, pp. 803-813. doi : 10.5802/alco.64. http://www.numdam.org/articles/10.5802/alco.64/

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