Schur congruences, Carlitz sequences of polynomials and automaticity Original Research Article

We first generalize the Schur congruence for Legendre polynomials to sequences of polynomials that we call ‘d-Carlitz’. This notion is more general than a similar notion introduced by Carlitz. Then, we study automaticity properties of double sequences generated by these sequences of polynomials, thus generalizing previous results on the double sequences produced by one-dimensional linear cellular automata.