Project Euler Forum

Can someone please explain to me what the meaning of:
1. $\tau^{-1}$
2. $\pi^k$

Of course! $\pi^k$ is the permutation arising from applying $\pi$ $k$ times. $\tau^{-1}$ is the inverse permutation of $\tau$. This is the notation used in, for example, https://en.wikipedia.org/wiki/Permutation#Definition.

Thanks! I just didn't know those signs

Note that in modern treatments permutations are usually formally defined as bijective functions. Although that's not the way you probably think of them if you were introduced to them (semi-)informally, it does help to clarify the notation: $\tau^{-1}$ is the inverse function, and $\pi^k$ is $k$-fold composition of a function with itself.

Hey admins, I would suggest adding a note or source on what k-fold compositions or inverse permutations are in problems 902 and 903. Especially in 903, it is quite difficult to understand how Q(2) is calculated. Even an example that solves for Q(2) would be sufficient.

raiden11 wrote: Wed Aug 14, 2024 5:04 pm Hey admins, I would suggest adding a note or source on what k-fold compositions or inverse permutations are in problems 902 and 903. Especially in 903, it is quite difficult to understand how Q(2) is calculated. Even an example that solves for Q(2) would be sufficient.

Thank you for the suggestion. We have discussed it in the team, and have added explicit definitions of $\tau^{-1}$ and $\pi^k$ to both problems.