Linear quantum addition rules
| dc.creator | Nathanson, Melvyn B. | |
| dc.date | 2006-03-27 | |
| dc.date.accessioned | 2026-07-07T07:07:15Z | |
| dc.date.available | 2026-07-07T07:07:15Z | |
| dc.description | 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. | |
| dc.description | 8 pages; to appear in Integers: The Electronic Journal of Combinatorial Number Theory | |
| dc.identifier | https://arxiv.org/abs/math/0603623 | |
| dc.identifier | http://arxiv.org/abs/math/0603623 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110323 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | 11B37, 11P81, 65Q05, 81R50,11B13 | |
| dc.title | Linear quantum addition rules | |
| dc.type | text |