Forbidden subposet problems in the grid

16 Feb 2021  ·  Dániel Gerbner, Dániel T. Nagy, Balázs Patkós, Máté Vizer ·

For posets $P$ and $Q$, extremal and saturation problems about weak and strong $P$-free subposets of $Q$ have been studied mostly in the case $Q$ is the Boolean poset $Q_n$, the poset of all subsets of an $n$-element set ordered by inclusion. In this paper, we study some instances of the problem with $Q$ being the grid, and its connections to the Boolean case and to the forbidden submatrix problem...

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