8 papers
Betti numbers of inductively pierced codes
Hugh Geller, Rebecca R. G., Alexandra Seceleanu +1
Neural ideals were introduced by Curto, Itskov, et al as an algebraic tool to study neural codes. In this paper, we use the notion of polarization introduced by Güntürkün, Jeffries…
Weighted Veronese Rings via Convex Semigroups
Bek Chase, Luca Fiorindo, Thiago Holleben +4
We determine properties of two-dimensional normal affine semigroup rings, and in particular of weighted Veronese rings, including determinantal presentation, Gröbner basis, graded…
Adjoints of Morphisms of Neural Codes
Juliann Geraci, Alexander B. Kunin, Alexandra Seceleanu
A combinatorial code is a collection of subsets of , or equivalently a set of points in . A morphism of codes is a map from one combinatorial code to…
Seshadri Regions and the Asymptotic Shape of Multigraded Regularity
Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi +1
We introduce the Seshadri region of a subvariety, a convex region packaging the classical Seshadri constants with respect to every line bundle simultaneously. We develop the theory…
The MacaulayPosets package for Macaulay2
Penelope Beall, Nikola Kuzmanovski, Yu Oliver Li +1
We introduce the package MacaulayPosets written for the computational algebra system Macaulay2. This package utilized the poset data type introduced in the Posets package and offer…
Boolean Rank via Monomial Ideals
Juliann Geraci, Alexander B. Kunin, Alexandra Seceleanu
Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean…
Constructions of Macaulay Posets and Macaulay Rings
Penelope Beall, Erenay Boyali, Nancy Chen +13
A poset is Macaulay if its partial order and an additional total order interact well. Analogously, a ring is Macaulay if the partial order defined on its monomials by division inte…
Lefschetz properties through a topological lens
Alexandra Seceleanu
These lecture notes were prepared for the Lefschetz Preparatory School, a graduate summer course held in Krakow, May 6-10, 2024. They present the story of the algebraic Lefschetz p…