On Popoviciu type tormulas for generalized restricted partition function
| dc.creator | Li, Nan | |
| dc.creator | Chen, Sheng | |
| dc.date | 2007-09-22 | |
| dc.date.accessioned | 2026-07-07T08:31:41Z | |
| dc.date.available | 2026-07-07T08:31:41Z | |
| dc.description | Suppose that $a_1(n),a_2(n),...,a_s(n),m(n)$ are integer-valued polynomials in $n$ with positive leading coefficients. This paper presents Popoviciu type formulas for the generalized restricted partition function $$p_{A(n)}(m(n)):=#\{(x_1,...,x_s)\in \mathbb{Z}^{s}: all x_j\geqslant 0, x_1a_1(n)+...+x_sa_s(n)=m(n) \}$$ when $s=2$ or 3. In either case, the formula implies that the function is an integer-valued quasi-polynomial. The main result is proved by a reciprocity law for a class of fractional part sums and the theory of generalized Euclidean division. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0709.3571 | |
| dc.identifier | http://arxiv.org/abs/0709.3571 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138570 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11D45, 05A15, 11P99 | |
| dc.title | On Popoviciu type tormulas for generalized restricted partition function | |
| dc.type | text |