On a Conjecture about the Number of Solutions to Linear Diophantine Equations with a Positive Integer Parameter
| dc.creator | Chen, Sheng | |
| dc.creator | Li, Nan | |
| dc.date | 2007-09-30 | |
| dc.date.accessioned | 2026-07-07T08:33:13Z | |
| dc.date.available | 2026-07-07T08:33:13Z | |
| dc.description | Let A(n) be a $k\times s$ matrix and $m(n)$ be a $k$ dimensional vector, where all entries of A(n) and $m(n)$ are integer-valued polynomials in $n$. Suppose that $$t(m(n)|A(n))=#\{x\in\mathbb{Z}_{+}^{s}\mid A(n)x=m(n)\}$$ is finite for each $n\in \mathbb{N}$, where $Z_+$ is the set of nonnegative integers. This paper conjectures that $t(m(n)|A(n))$ is an integer-valued quasi-polynomial in $n$ for $n$ sufficiently large and verifies the conjecture in several cases. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0710.0177 | |
| dc.identifier | http://arxiv.org/abs/0710.0177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139052 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05A15; 11D45; 11P99 | |
| dc.title | On a Conjecture about the Number of Solutions to Linear Diophantine Equations with a Positive Integer Parameter | |
| dc.type | text |