I'm working on this permutation and write that in terms of disjoint cycles: $(7236)(85)(571)(1537)(486)$. Since $(1537)$ and $(486)$ are disjoint, I computed the 3 middle cycles from right to left and obtained $(17853)$. i.e. $(7236)(17853)(486)$. Now does that matter which two cycles I should compute first? Does $\tau\circ \sigma\circ \delta= \tau(\sigma(\delta)?$ Thanks!
2026-03-27 21:19:08.1774646348
Express a product of disjoint cycles.
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No, the order in which you perform the computations does not matter. This is because composition (the operation from which “cycle product” stems) is associative - this means $f \circ (g \circ h) = (f \circ g) \circ h$.
In your case, you can put the parenthesis around the middle terms in order to perform those products first.