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Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.
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Counting Selections of Entries such having an Extremal Permutation of length n^2+1
Let $S_{n^2+1}$ be permutations of length $n^2+1$. By Erdos-Szekeres Theorem. any $s \in S_{n^2+1}$ would have a monotone subsequence(increasing or decreasing)of length $n+1$. … For example:
Let $E_4=\{1,2,3,8\}$
This $E_4$ has an extremal permutations $s_{10}=(4,3,2,7,6,10,9,1,5,8)$. The monotone subsequence is $(4,3,2,1)$ which is located at $E_4=(1,2,3,8)$. …