-cluster-free families of subspaces

G Currier, S Shahriari - arXiv preprint arXiv:2403.04895, 2024 - arxiv.org
Three $ k $-dimensional subspaces $ A $, $ B $, and $ C $ of an $ n $-dimensional vector
space $ V $ over a finite field are called a $3 $-cluster if $ A\cap B\cap C=\{\mathbf {0} _V\} …

On forbidden poset problems in the linear lattice

J Xiao, C Tompkins - arXiv preprint arXiv:1905.09246, 2019 - arxiv.org
In this note, we determine the maximum size of a $\{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 …

[PDF][PDF] PROBLEMS IN EXTREMAL SET THEORY/PROBLÉMÁK AZ EXTREMÁLIS HALMAZRENDSZEREK TÉMAKÖRÉBŐL

B Patkós - 2022 - real-d.mtak.hu
Erdos Pál és Daniel Kleitman egy 1970-es egy konferenciakötetben megjeleno cikkükben
[17] a következoképpen foglalták össze, hogy mely muveletek természetesek az extremális …

The covering lemma and -analogues of extremal set theory problems

D Gerbner - arXiv preprint arXiv:1905.06994, 2019 - arxiv.org
We prove a general lemma (inspired by a lemma of Holroyd and Talbot) about the
connection of the largest cardinalities (or weight) of structures satisfying some hereditary …