Quadratic addition rules for quantum integers Original Research Article

For every positive integer n, the quantum integer [n]q is the polynomial [n]q=1+q+q2+cdots, three dots, centered+qn-1. A quadratic addition rule for quantum integers consists of sequences of polynomials image, image, and image such that image for all m and n. This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials image that satisfy the associated functional equation image.