Quadratic Addition Rules for Quantum Integers

  title={Quadratic Addition Rules for Quantum Integers},
  author={Melvyn B. Nathanson},
For every positive integer n, the quantum integer [n]q is the polynomial [n]q = 1 + q + q + · · · + q. A quadratic addition rule for quantum integers consists of sequences of polynomials R = {r n (q)} n=1 , S = {s n (q)} n=1 , and T ′ = {t m,n (q)} m,n=1 such that [m + n]q = r n(q)[m]q + s m (q)[n]q + t′m,n(q)[m]q [n]q for all m and n. This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials F = {fn(q)}∞n=1 that satisfy the associated… CONTINUE READING