We prove that for every integer $d \geq 3$, there exists $α<1$ such that the maximum dimension of an $n$-element poset containing no standard example of order $d$ as an induced subposet is $\mathcal{O}_d(n^α)$. For $d=3$, we obtain an upper bound $\mathcal{O}...
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RESEARCH
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TECHNICAL
On dimension of posets excluding a standard example
We prove that for every integer $d \geq 3$, there exists $α<1$ such that the maximum dimension of an $n$-element poset containing no standard example of order $d$ as an induced subposet is $\mathcal{O}_d(n^α)$. For $d=3$, we obtain an upper bound $\mathcal{O}...
We prove that for every integer $d \geq 3$, there exists $α<1$ such that the maximum dimension of an $n$-element poset containing no standard example of order $d$ as an induced subposet is $\mathcal{O}_d(n^α)$. For $d=3$, we obtain an upper bound $\mathcal{O}(n^{2/3}\log n)$, while we also construct a family of...
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Signal Strength 95%
Technical label SOURCE-BACKED
Public Interest 32
Category RESEARCH
Reader Depth TECHNICAL
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Consequence Score 18
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