On Forbidden Poset Problems in the Linear Lattice

  • Jimeng Xiao
  • Casey Tompkins


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.  

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