arXiv subjects

José Alejandro Samper

Publications and source records attributed to José Alejandro Samper.

6 recordsLinked to original sources

arXiv2026

Characterization of Stanley-Reisner varieties by their automorphism group

We study the automorphism ind-group of a Stanley-Reisner variety $X_Δ$ through a combinatorial toolkit on the underlying complex: a facet closure operator, its Demazure roots, and the resulting dichotomy between exposed and hidden facets. Our main theorem is that a fully exposed complex, that is, one in which every facet has a private vertex, is recovered from the ind-group: $\mathrm{Aut}(X_Δ)\cong\mathrm{Aut}(X_{Δ'})$ forces $Δ\congΔ'$. The hypothesis cannot be dropped, but it holds after one stabilization, so for arbitrary $Δ,Δ'$ an isomorphism $\mathrm{Aut}(X_Δ\times\mathbb{A}^1)\cong\mathrm{Aut}(X_{Δ'}\times\mathbb{A}^1)$ already forces $Δ\congΔ'$. At the opposite extreme, a fully hidden $Δ$ gives $\mathrm{Aut}(X_Δ)=T_0\rtimes S(Δ)$, never isomorphic to the ind-group of a non-rigid Stanley-Reisner variety. The criterion decides graphs and skeleta, and every complex is homotopy equivalent to a fully exposed one.

math.AG↗

arXiv2026

Poset Partitions and the Combinatorics of the $\textbf{cd}$-Index

We introduce a new class of Eulerian posets, called S-partitionable posets, which have a non-negative cd-index. These posets are a generalization of S-shellable complexes introduced by Stanley in 1994. We prove that S-partitionable posets have a non-negative cd-index via a recursive formula. Then, we introduce a semi-Eulerian version of S-partitionable posets, which we call SE-partitionable posets. We show that SE-partitionable posets also have a non-negative semi-Eulerian cd-index as defined by Juhnke-Kubitzke, Samper and Venturello in 2024.

math.CO↗

arXiv2025

Discrete Curvatures and Convex Polytopes

We study Forman--Ricci and effective resistance curvatures on the skeleta of convex polytopes. Our guiding questions are: how frequently do polytopal graphs exhibit everywhere positive curvature, and what structural constraints does positivity impose? For Forman--Ricci curvature we derive an exact identity for the average edge curvature in terms of flag $f$-numbers and establish the existence of infinite families of Forman--Ricci-positive polytopes in every fixed dimension $d\ge 6$. We prove finiteness results in low dimension: there are only finitely many Forman--Ricci-positive $3$- and $4$-polytopes; for $d=5$ we show finiteness in the simplicial case, and conjecture its extension to $5$-polytopes more generally. For the resistance curvature $κ(v)$ we establish the existence of infinite families for all $d\ge 3$, and we provide a quantitative lower bound for $κ(v)$ in a simple $3$-polytope in terms of the lengths of the three $2$-faces incident to $v$. This bound leads to constructions of non-vertex-transitive, resistance-positive $3$-polytopes via $Δ$-operations, and a degree-based obstruction showing that if each neighbor of $v$ has degree at most $d_v-2$, then $κ(v)\le 0$. Our results suggest that positive curvature on polytopal skeletons is rare and constrained.

math.CO↗

arXiv2024

The $cd$-index of semi-Eulerian posets

We generalize the definition of the $cd$-index of an Eulerian poset to the class of semi-Eulerian posets. For simplicial semi-Eulerian Buchsbaum posets, we show that all coefficients of the $cd$-index are non-negative. This proves a conjecture of Novik for odd dimensional manifolds and extends it to the even dimensional case.

math.CO↗

arXiv2021

Reciprocal maximum likelihood degrees of diagonal linear concentration models

We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model $\mathcal L \subseteq \mathbb{C}^n$ of dimension $r$ is equal to $(-2)^rχ_M( \textstyle\frac{1}{2})$, where $χ_M$ is the characteristic polynomial of the matroid $M$ associated to $\mathcal L$. In particular, this establishes the polynomiality of the rmld for general diagonal linear concentration models, positively answering a question of Sturmfels, Timme, and Zwiernik.

math.ST↗

arXiv2016

A Geometric Lower Bound Theorem

We resolve a conjecture of Kalai relating approximation theory of convex bodies by simplicial polytopes to the face numbers and primitive Betti numbers of these polytopes and their toric varieties. The proof uses higher notions of chordality. Further, for C^2-convex bodies, asymptotically tight lower bounds on the g-numbers of the approximating polytopes are given, in terms of their Hausdorff distance from the convex body.

math.MG↗