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arXiv · 1905.09246

On forbidden poset problems in the linear lattice

Jimeng Xiao·Casey Tompkins
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Abstract

In this note, we determine the maximum size of a $\{V_{k}, Λ_{l}\}$-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.

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Jimeng Xiao, Casey Tompkins. 2019-10-09. On forbidden poset problems in the linear lattice. https://arxiv.org/abs/1905.09246

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