Séminaire d'algèbre et de géométrie du 20-03-2025

Exposé de Mehrdad Nasernejad

Le 20-03-2025 à 14:00, en P108 et en ligne.

Classes of MFMC and minimally non-MFMC clutters

Informations de connexion

Zoom: https://univ-artois-fr.zoom.us/j/96746097273

Résumé

Let I ⊂ R=K[x₁,..,x_n] be a square-free monomial ideal, q be a monomial prime ideal in R, h be a square-free monomial in R with supp(h) ∩ supp(q) ∪ supp(I)= ∅, and define L:=I ∩ (q,h). In this talk, which is based on NCH, we first discuss, under certain conditions, whether the associated clutter of L has the MFMC property. In particular, we provide an application to a combinatorial result. Next, we introduce a class of square-free monomial ideals whose associated clutters are minimally non-MFMC.

NCH: M. Nasernejad, V. Crispin Quinonez, and W. Hochstättler, On the normally torsion-freeness of square-free monomial ideals, 2025, Journal of Algebra and its Applications.