1 results
GENERATING FUNCTIONS FOR THE QUOTIENTS OF NUMERICAL SEMIGROUPS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 110 / Issue 3 / December 2024
- Published online by Cambridge University Press:
- 29 February 2024, pp. 427-438
- Print publication:
- December 2024
-
- Article
-
- You have access
- HTML
- Export citation
-
We propose generating functions,
$\textrm {RGF}_p(x)$, for the quotients of numerical semigroups which are related to the Sylvester denumerant. Using MacMahon’s partition analysis, we can obtain 
$\textrm {RGF}_p(x)$ by extracting the constant term of a rational function. We use 
$\textrm {RGF}_p(x)$ to give a system of generators for the quotient of the numerical semigroup 
$\langle a_1,a_2,a_3\rangle $ by p for a small positive integer p, and we characterise the generators of 
${\langle A\rangle }/{p}$ for a general numerical semigroup A and any positive integer p.
