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Let $a_1a_2\ldots a_{2n+1}$ ($n\geq 2$) be a given permutation of the numbers from $1$ to $2n+1$ and let $\alpha_i=\{i,i+1,i+2\},~1\leq i\leq 2n-1$ $\alpha_{2n}=\{2n,2n+1,1\}$ $\alpha_{2n+1}=\{2n+1,1,...

This question is related to my other question Sign of the permutation which brings a subsequence back to its original form. Suppose I have a complete ordered set $\{a_{1},\dotsc,a_{2n}\}$ and take $\...

I have the following question, which I am thinking about for days now and can't get the answer right. I have a sequence of elements in this order $x_{1},x_{2},...,x_{2n}$, $n \ge 1$ and then I perform ...

This will not be altogether unrelated to this earlier question. For which classes $C$ of bijections from $\{1,2,3,\ldots\}$ to itself is it the case that for all sequences $\{a_i\}_{i=1}^\infty$ of ...