Properties of Multivariate b-Ary Stern Polynomials

Given an integer base b = 2, we investigate a multivariate b-ary polynomial analogue of Stern's diatomic sequence which arose in the study of hyper b-ary representations of integers. We derive various properties of these polynomials, including a generating function and identities that lead to factorizations of the polynomials. We use some of these results to extend an identity of Courtright and Sellers on the b-ary Stern numbers sb(n). We also extend a result of Defant and a result of Coons and Spiegelhofer on the maximal values of sb(n) within certain intervals. Mathematics Subject Classification. Primary 05A15; Secondary 11B83.