Year: 2026
Type: preprint
Abstract: We determine explicit formulae for the Betti numbers of the defining toric ideals of two families of numerical semigroups of Sally type, resolving and extending beyond several conjectures of Goel--Şahin--Singh--Srinivasan. Our approach uses Apéry resolutions and their specialisations. For the family \[ Γ_m(n)=\langle m,m+1,\ldots,\widehat{m+n},\ldots,2m-1\rangle, \qquad 2\leq n
Source: arXiv (Cornell University)
Institution: Purdue University West Lafayette
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214121735