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Sponsored AI Networking Cookbook: Practical recipes for AI-assisted network automation and development AI Networking Cookbook: Practical recipes for AI-assisted network automation and development

Author

Manohar Kumar

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Preprint Sep 2026

The Betti numbers and Golodness of numerical semigroup rings of Sally type

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--\c{S}ahin--Singh--Srinivasan. Our approach uses Ap\'ery resolutions and their specialisations. For the family \[ \Gamma_m(n...

Manav Batavia, Omkar Javadekar, Manohar Kumar · 0 citations
Preprint Aug 2026

$\mathrm{v}$-number of Lov\'asz-Saks-Schrijver Ideals and (parity) binomial edge ideals of graphs

In this paper, we introduce a new framework for computing certain localized $\mathrm{v}$-numbers of a class of ideals called coordinate-saturated ideals, which includes certain classes of Lov\'asz-Saks-Schrijver (LSS) ideals and (generalized) binomial edge ideals associated with graphs. For a forest graph $G$, we deriv...

Manohar Kumar, Emiliano Liwski · 0 citations

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