# ALGEBRAIC COMBINATORICS

Higher nerves of simplicial complexes
Algebraic Combinatorics, Volume 2 (2019) no. 5, p. 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 $k\left[\Delta \right]$ as well as the $f$-vector and $h$-vector of $\Delta$. We present, as an application, a formula for computing regularity of monomial ideals.

Revised : 2019-01-29
Accepted : 2019-01-29
Published online : 2019-10-08
DOI : https://doi.org/10.5802/alco.64
Classification:  05E40,  05E45,  13C15,  13D03
Keywords: Nerve Complex, depth, $k$-connectivity, homologies, poset, monomial ideals
@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},
publisher = {MathOA foundation},
volume = {2},
number = {5},
year = {2019},
pages = {803-813},
doi = {10.5802/alco.64},
language = {en},
url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_5_803_0}
}

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/item/ALCO_2019__2_5_803_0/

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