Down and Out in Paris and London
To my knowledge, there was never any collaboration between Perma and Avon. Perma P267 was printed in 1953; Avon T-121 appeared in 1956. The illustration was painted by George Erickson. The picture, in itself, is not so odd. Hardcover publishers had a lot of pull when it came to placing limits on paperback reprints. Keep in mind that Doubleday's reason for starting Perma Books was to easily roll its hardcover publications into paperback. (In 1954, Doubleday sold Perma to Pocket Books.) How the rights wound up with Avon isn't really important.
Of real interest is the yellow printing on the cover. It's identical. It's obvious to me that Avon didn't just use the same illustration here. THEY MADE A COPY OF THE COVER OF THE PERMA BOOK! The other writing on the Perma cover has simply been cropped out.