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- W1703626961 abstract "Let $F$ be a family of subsets of ${1,ldots,n}$. We say that $F$ is $P$-free if the inclusion order on $F$ does not contain $P$ as an induced subposet. The emph{Tur'an function} of $P$, denoted $pi^*(n,P)$, is the maximum size of a $P$-free family of subsets of ${1,ldots,n}$. We show that $pi^*(n,P) le (4r + O(sqrt{r}))binom{n}{n/2}$ if $P$ is an $r$-element poset of height at most $2$. We also show that $pi^*(n,S_r) = (r+O(sqrt{r}))binom{n}{n/2}$ where $S_r$ is the standard example on $2r$ elements, and that $pi^*(n,B_2) le (2.583+o(1))binom{n}{n/2}$, where $B_2$ is the $2$-dimensional Boolean lattice." @default.
- W1703626961 created "2016-06-24" @default.
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- W1703626961 date "2014-08-04" @default.
- W1703626961 modified "2023-09-23" @default.
- W1703626961 title "Set families with forbidden subposets" @default.
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- W1703626961 doi "https://doi.org/10.48550/arxiv.1408.0646" @default.
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