Rational generating function conjecture for the class of permutations corresponding to pin words

A pin word is a word encoding a permutation through the pin sequence construction; the set of permutations corresponding to pin words forms a permutation class. Rational generating function conjecture. The class of permutations corresponding to pin words has a rational generating function. This conjecture concerns the enumerative structure of the permutation class arising from pin words and reflects the regular-language origin of the class. The supplied text gives no evidence of resolution.