Hyperbinary Expansions and Stern Polynomials
نویسندگان
چکیده
We introduce an infinite class of polynomial sequences at(n; z) with integer parameter t > 1, which reduce to the well-known Stern (diatomic) sequence when z = 1 and are (0, 1)-polynomials when t > 2. Using these polynomial sequences, we derive two different characterizations of all hyperbinary expansions of an integer n > 1. Furthermore, we study the polynomials at(n; z) as objects in their own right, obtaining a generating function and some consequences. We also prove results on the structure of these sequences, and determine expressions for the degrees of the polynomials.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015