In this note, we determine the maximum size of a $\{\mathrm{V}_{k}, \Lambda_{l}\}$-free family in the lattice of vector subspaces of a finite vector space both in the non-induced case as well as the induced case, for a large range of parameters $k$ and $l$. These results generalize earlier work by Shahriari and Yu. We also prove a general LYM-type lemma for the linear lattice which resolves a conjecture of Shahriari and Yu.
@article{10_37236_8831,
author = {Jimeng Xiao and Casey Tompkins},
title = {On forbidden poset problems in the linear lattice},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/8831},
zbl = {1433.06001},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8831/}
}
TY - JOUR
AU - Jimeng Xiao
AU - Casey Tompkins
TI - On forbidden poset problems in the linear lattice
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8831/
DO - 10.37236/8831
ID - 10_37236_8831
ER -
%0 Journal Article
%A Jimeng Xiao
%A Casey Tompkins
%T On forbidden poset problems in the linear lattice
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8831/
%R 10.37236/8831
%F 10_37236_8831
Jimeng Xiao; Casey Tompkins. On forbidden poset problems in the linear lattice. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8831
