Zobrazeno 1 - 10
of 130
pro vyhledávání: '"Fink, Alex"'
A "tropical ideal" is an ideal in the idempotent semiring of tropical polynomials that is also, degree by degree, a tropical linear space. We introduce a construction based on transversal matroids that canonically extends any principal ideal to a tro
Externí odkaz:
http://arxiv.org/abs/2405.16338
Autor:
Fink, Alex, Olarte, Jorge Alberto
Following up on our previous work, we study single-element extensions of transversal valuated matroids. We show that tropical presentations of valuated matroids with a minimal set of finite entries enjoy counterparts of the properties proved by Bonin
Externí odkaz:
http://arxiv.org/abs/2308.05556
We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the volume and lattice point counts of type B generalized permutohedra. Appl
Externí odkaz:
http://arxiv.org/abs/2209.06752
Matroids and the space of torus-invariant subvarieties of the Grassmannian with given homology class
Let $\mathbb{G}(d,n)$ be the complex Grassmannian of affine $d$-planes in $n$-space. We study the problem of characterizing the set of algebraic subvarieties of $\mathbb{G}(d,n)$ invariant under the action of the maximal torus $T$ and having given ho
Externí odkaz:
http://arxiv.org/abs/2112.15334
We study a class of combinatorially-defined polynomial ideals which are generated by minors of a generic symmetric matrix. Included within this class are the symmetric determinantal ideals, the symmetric ladder determinantal ideals, and the symmetric
Externí odkaz:
http://arxiv.org/abs/2104.09589
Autor:
Fink, Alex, Toghani, Zeinab
Publikováno v:
Pacific J. Math. 318 (2022) 453-468
We show that solution sets of systems of tropical differential equations can be characterised in terms of monomial-freeness of an initial ideal. We discuss a candidate definition of tropical differential basis and give a nonexistence result for such
Externí odkaz:
http://arxiv.org/abs/2004.08258
Autor:
Berget, Andrew, Fink, Alex
The group $G = GL_r(k) \times (k^\times)^n$ acts on $\mathbf{A}^{r \times n}$, the space of $r$-by-$n$ matrices: $GL_r(k)$ acts by row operations and $(k^\times)^n$ scales columns. A matrix orbit closure is the Zariski closure of a point orbit for th
Externí odkaz:
http://arxiv.org/abs/1904.10047
We prove that if $\sigma \in S_m$ is a pattern of $w \in S_n$, then we can express the Schubert polynomial $\mathfrak{S}_w$ as a monomial times $\mathfrak{S}_\sigma$ (in reindexed variables) plus a polynomial with nonnegative coefficients. This impli
Externí odkaz:
http://arxiv.org/abs/1903.10332
Autor:
Fink, Alex, Olarte, Jorge Alberto
Given $d$ row vectors of $n$ tropical numbers, $d
Externí odkaz:
http://arxiv.org/abs/1903.08288
Autor:
Cameron, Amanda, Fink, Alex
We recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhart-style polynomial counting lattice points in the Minkowski sum of its base polytope and scalings of simplices. Our polynomial has coefficients of alternating si
Externí odkaz:
http://arxiv.org/abs/1802.09859