Geodesic
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

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{ALCO_2019__2_5_803_0,
     author = {Dao, Hailong and Doolittle, Joseph and Duna, Ken and Goeckner, Bennet and Holmes, Brent and Lyle, Justin},
     title = {Higher nerves of simplicial complexes},
     journal = {Algebraic Combinatorics},
     pages = {803--813},
     publisher = {MathOA foundation},
     volume = {2},
     number = {5},
     year = {2019},
     doi = {10.5802/alco.64},
     mrnumber = {4023567},
     zbl = {1421.05099},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/alco.64/}
}
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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

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