(b) The hinted labeling, call it *P*(*c*), has 1s on the path corresponding to *c*, and 0s elsewhere; thus it is balanced. The general animating function can be written

so it is balanced if and only if *c _{m}* = 0.

[Incidentally, the set *S* = {*P*(0)} ∪ {*P*(*k*) ⊕ *P*(*k* + 2* ^{e}*) |

(c) The function *P*(*c*) in (b) has this form, because *x*^{P(c)} = *x* ⊕ *x* ⊕ *c*. Its inverse, *x*^{S(c)} = ((*x* ⊕ *c*) + ...

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