# Wheres is this method/notation of option portfolio payoff design from?

The "desired position" in the image is a set of slopes $$(0,1,-1,0)$$, and a set of strike prices between these slopes $$\mathbf{K}=(98,100,102)$$.

The payoff is then designed by finding the positions $$n_1,n_2,n_3$$ in three call options

$$c_1=(0,1,1,1)\mathbf{K}$$ $$c_2=(0,0,1,1)\mathbf{K}$$ $$c_3=(0,0,0,1)\mathbf{K}$$

So that they total the desired payoff $$(0,1,-1,0)$$.

In this case of a butterfly spread, the required postions are $$n_1=1$$ $$n_2=-2$$ and $$n_3=1$$.

Any points to litterature where this method is used is appreciated.