4 citations · 10 across the 9 of their papers we have counts for
9 papers
Linear Degenerate Tropical Flag Varieties
Alessio Borzì, Victoria Schleis
We study linear degenerations of flag varieties from the point of view of tropical geometry. We define the linear degenerate flag Dressian and prove a correspondence between: …
Tropical computations for toric intersection theory in Macaulay2
Alessio Borzì
We present the Macaulay2 package TropicalToric.m2 for toric intersection theory computations using tropical geometry.
The leading coefficient of Lascoux polynomials
Alessio Borzí, Xiangying Chen, Harshit J. Motwani +2
Lascoux polynomials have been recently introduced to prove polynomiality of the maximum-likelihood degree of linear concentration models. We find the leading coefficient of the Las…
Weierstrass sets on finite graphs
Alessio Borzì
We study two possible tropical analogues of Weierstrass semigroups on graphs, called rank and functional Weierstrass sets. We prove that on simple graphs, the first is contained in…
Cyclotomic numerical semigroup polynomials with at most two irreducible factors
Alessio Borzì, Andrés Herrera-Poyatos, Pieter Moree
A numerical semigroup is cyclotomic if its semigroup polynomial is a product of cyclotomic polynomials. The number of irreducible factors of (with multiplicity) is…
Graded algebras with cyclotomic Hilbert series
Alessio Borzì, Alessio D'Alì
Let be a positively graded algebra over a field. We say that is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. S…
Set of independencies and Tutte polynomial of matroids over a domain
Alessio Borzì, Ivan Martino
In this work, we study matroids over a domain and several classical combinatorial and algebraic invariants related. We define their Grothendieck-Tutte polynomial $T_{\mathcal{M}}(x…
Patterns on the numerical duplication by their admissibility degree
Alessio Borzì
We develop the theory of patterns on numerical semigroups in terms of the admissibility degree. We prove that the Arf pattern induces every strongly admissible pattern, and determi…
A characterization of the Arf property for quadratic quotients of the Rees algebra
Alessio Borzì
We provide a characterization of the Arf property in both the numerical duplication of a numerical semigroup and in a member of a family of quotients of the Rees algebra studied in…