17 citations · 53 across the 26 of their papers we have counts for
31 papers
The symbolic and divisorial analytic spreads are finite
Jonathan Montaño
Let be a ring that is essentially of finite type over a field and be an ideal. In this article it is shown that the minimal number of generators of the symbolic…
The multiplicity sequence of monomial ideals
Sudipta Das, Jonathan Montaño, Aniketh Sivakumar
We give a convex-geometric formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron. We also construc…
Matroid correspondence
Colin Crowley, Changxin Ding, Haoxi Hu +7
Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues.…
Homology of Vietoris-Rips complexes of hypercube graphs via group actions
Federico Galetto, Jonathan Montaño, Zoe Wellner
The Vietoris-Rips complex of a metric space is the simplicial complex whose faces are the subsets of points with pairwise distance bounded above by a given scale . In this paper…
Ladder determinantal varieties and their symbolic blowups
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt +2
In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly -regular. Furthermore, we prove that the symbolic associated graded alge…
The core of monomial ideals
Louiza Fouli, Jonathan Montaño, Claudia Polini +1
The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal satisfying certa…
K-polynomials of multiplicity-free varieties
Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi +1
We describe the twisted -polynomial of multiplicity-free varieties in a multiprojective setting. More precisely, for multiplicity-free varieties, we show that the support of the…
Purity of monoids and characteristic-free splittings in semigroup rings
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt
Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singulari…
Frobenius methods in combinatorics
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt
We survey results produced from the interaction between methods in prime characteristic and combinatorial commutative algebra. We showcase results for edge ideals, toric varieties,…
Double Schubert polynomials do have saturated Newton polytopes
Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi +1
We prove that double Schubert polynomials have the Saturated Newton Polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory…
Blowup algebras of determinantal ideals in prime characteristic
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt
We study when blowup algebras are -split or strongly -regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a…
Computing multiplicity sequences
Justin Chen, Youngsu Kim, Jonathan Montaño
The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomia…
Mixed multiplicities of graded families of ideals
Yairon Cid-Ruiz, Jonathan Montaño
We show the existence (and define) the mixed multiplicities of arbitrary graded families of ideals under mild assumptions. In particular, our methods and results are valid for the…
Convex bodies and graded families of monomial ideals
Yairon Cid-Ruiz, Jonathan Montaño
We show that the mixed volumes of arbitrary convex bodies are equal to mixed multiplicities of graded families of monomial ideals, and to normalized limits of mixed multiplicities…
Exterior powers and Tor-persistence
Justin Lyle, Jonathan Montaño, Keri Sather-Wagstaff
A commutative Noetherian ring is said to be Tor-persistent if, for any finitely generated -module , the vanishing of for implies $M…
Improving Locality Sensitive Hashing by Efficiently Finding Projected Nearest Neighbors
Omid Jafari, Parth Nagarkar, Jonathan Montaño
Similarity search in high-dimensional spaces is an important task for many multimedia applications. Due to the notorious curse of dimensionality, approximate nearest neighbor techn…
When are multidegrees positive?
Federico Castillo, Yairon Cid-Ruiz, Binglin Li +2
Let be an arbitrary field, be a multiprojective space over , and be a closed subscheme of . We provide…
Symbolic powers of determinantal ideals in prime characteristic
Jonathan Montaño, Luis Núñez-Betancourt
We study the symbolic powers of determinantal ideals of generic, generic symmetric, and Hankel matrices of variables, and of Pfaffians of generic skew-symmetric matrices, in prime…
Analytic spread and integral closure of integrally decomposable modules
Carles Bivià-Ausina, Jonathan Montaño
We relate the analytic spread of a module expressed as the direct sum of two submodules with the analytic spread of its components. We also study a class of submodules whose integr…
Efficient Bitmap-based Indexing and Retrieval of Similarity Search Image Queries
Omid Jafari, Parth Nagarkar, Jonathan Montaño
Finding similar images is a necessary operation in many multimedia applications. Images are often represented and stored as a set of high-dimensional features, which are extracted…
Symbolic analytic spread: upper bounds and applications
Hailong Dao, Jonathan Montaño
The symbolic analytic spread of an ideal is defined in terms of the rate of growth of the minimal number of generators of its symbolic powers. In this article we find upper bou…
Extremal growth of Betti numbers and trivial vanishing of (co)homology
Justin Lyle, Jonathan Montaño
A Cohen-Macaulay local ring satisfies trivial vanishing if for all large implies or has finite projective dimension. If satisfie…
On asymptotic vanishing behavior of local cohomology
Hailong Dao, Jonathan Montaño
Let be a standard graded algebra over a field , with irrelevant maximal ideal $\fm$, and a homogeneous -ideal. We study the asymptotic vanishing behavior of the grade…
Splittings and symbolic powers of square-free monomial Ideals
Jonathan Montaño, Luis Núñez-Betancourt
We study the symbolic powers of square-free monomial ideals via symbolic Rees algebras and methods in prime characteristic. In particular, we prove that the symbolic Rees algebra a…