Notation for breaking sets into pairs

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I am preparing some notes on Wick's theorem. Let $i_1,\dots,i_{2m}\in\{1,\dots,N\}.$ Is there any standard notation for the set of all sets of the form $\{(i_1^1,i_1^2),(i_2^1,i_2^2),\dots,(i_m^1,i_m^2)\}$ such that $(i_1^1,i_1^2,i_2^1,i_2^2,\dots,i_m^1,i_m^2)=(i_{\sigma(1)},\dots,i_{\sigma(2m)})$ for some permutation $\sigma\in S_{2m}$? Just for curiosity.