We prove some new rank selection theorems for balanced simplicial complexes. Specifically, we prove that if a balanced simplicial complex satisfies Serre's condition $(S_{\ell})$ then so do all of its rank selected subcomplexes. We also provide a formula for the depth of a balanced simplicial complex in terms of reduced homologies of its rank selected subcomplexes. By passing to a barycentric subdivision, our results give information about Serre's condition and the depth of any simplicial complex. Our results extend rank selection theorems for depth proved by Stanley, Munkres, and Hibi.
@article{10_37236_9299,
author = {Brent Holmes and Justin Lyle},
title = {Rank selection and depth conditions for balanced simplicial complexes},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {2},
doi = {10.37236/9299},
zbl = {1465.05197},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9299/}
}
TY - JOUR
AU - Brent Holmes
AU - Justin Lyle
TI - Rank selection and depth conditions for balanced simplicial complexes
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9299/
DO - 10.37236/9299
ID - 10_37236_9299
ER -
%0 Journal Article
%A Brent Holmes
%A Justin Lyle
%T Rank selection and depth conditions for balanced simplicial complexes
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9299/
%R 10.37236/9299
%F 10_37236_9299
Brent Holmes; Justin Lyle. Rank selection and depth conditions for balanced simplicial complexes. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9299
