Linear quantum addition rules

Details Linear quantum addition rules Linear quantum addition rules

2006-03-27

arxiv.org/abs/math/0603623v1

Mathematics

Number Theory

8 pages; to appear in Integers: The Electronic Journal of Combinatorial Number Theory

Scientific paper

The quantum integer $[n]_q$ is the polynomial $1 + q + q^2 + ... + q^{n-1}.$ Two sequences of polynomials $\mathcal{U} = \{u_n(q)\}_{n=1}^{\infty}$ and $\mathcal{V} = \{v_n(q)\}_{n=1}^{\infty}$ define a {\em linear addition rule} $\oplus$ on a sequence $\mathcal{F} = \{f_n(q)\}_{n=1}^{\infty}$ by $f_m(q)\oplus f_n(q) = u_n(q)f_m(q) + v_m(q)f_n(q).$ This is called a {\em quantum addition rule} if $[m]_q \oplus [n]_q = [m+n]_q$ for all positive integers $m$ and $n$. In this paper all linear quantum addition rules are determined, and all solutions of the corresponding functional equations $f_m(q)\oplus f_n(q) = f_{m+n}(q)$ are computed.

Affiliated with

Also associated with

No associations

Rating

Linear quantum addition rules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Linear quantum addition rules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear quantum addition rules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-413639