Simplifying Equation - Quantum String

Question

In this post Quantum String action , the user does the following manipulation :
$$delta (H_{mnp})H^{mnp} =partial_mdelta(B_{np})[H^{mnp}+H^{pmn}+H^{npm}] $$
I can't quite understand how he does that, I get where the derivative comes from but how does it appear three combinations of $H^{mnp}$?

Urb · Accepted Answer

If $H_{mnp}=partial_m B_{np}+partial_n B_{pm}+partial_p B_{mn}$, then
$$delta(H_{mnp})=partial_m(delta B_{np})+partial_n(delta B_{pm})+partial_p(delta B_{mn})$$
and
begin{align}
delta (H_{mnp})H^{mnp} &=left[partial_m(delta B_{np})+partial_n(delta B_{pm})+partial_p(delta B_{mn})right]H^{mnp}
&=partial_m(delta B_{np})H^{mnp}+partial_n(delta B_{pm})H^{mnp}+partial_p(delta B_{mn})H^{mnp}
&=partial_m(delta B_{np})H^{mnp}+partial_m(delta B_{np})H^{pmn}+partial_m(delta B_{np})H^{npm}
&=partial_m(delta B_{np})left[H^{mnp}+H^{pmn}+H^{npm}right].
end{align}
So it's just a matter of renaming indices in the last two terms.

Simplifying Equation - Quantum String

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