Answer by Mike Earnest for Show that permutations of $n$ have no increasing...
Here is a proof that $\lceil \sqrt n\rceil$ is the best result possible, for all $n$.Given $n$, let $s=\lceil \sqrt n\rceil$. Note that $s^2$ is the smallest perfect square which is greater than or...
View ArticleShow that permutations of $n$ have no increasing or decreasing sequences...
While doing Pigeonhole principle in our class, our professor mentioned and proved that every permutation of $n$ either has a decreasing or an increasing subsequence of length ⌈$\sqrt n$⌉.But how do I...
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