When a painting is printed as a limited edition print by a publisher, ten percent of the edition is reserved for the artist and are called Artist Proofs. For example if the edition size is 850 prints, the artist will get 85. These prints are signed by the artist and would be numbered from 1/85 AP to 85/85 AP.
Pricing is determined by the number of prints available for sale. If the regular edition has not sold out, then the price for the AP is the same as the regular print. When the regular edition has sold out, then the price goes up as the number of prints available for sale declines.
A note of low inventory means that there are less than 30 prints total of that image available for sale. A note of very low inventory means that there are less than 10.