Related papers: Weak Orientability of Matroids and Polynomial Equa…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
We introduce greedy weights of matroids, inspired by those for linear codes. We show that a Wei duality holds for two of these types of greedy weights for matroids. Moreover we show that in the cases where the matroids involved are…
We settle three problems from the literature on stable and real zero polynomials and their connection to matroid theory. We disprove the weak real zero amalgamation conjecture by Schweighofer and the second author. We disprove a conjecture…
The control and sensing of large-scale systems results in combinatorial problems not only for sensor and actuator placement but also for scheduling or observability/controllability. Such combinatorial constraints in system design and…
We propose a model for recoverable robust optimization with commitment. Given a combinatorial optimization problem and uncertainty about elements that may fail, we ask for a robust solution that, after the failing elements are revealed, can…
Let K be the face ring of the independence complex of a matroid. We show that if T is a generic linear system of parameters, then K/T satisfies a weak form of the Hard Lefschetz Theorem. As a result, the first half of the h-vector of the…
This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power…
We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its…
If V(R) is the vertex set of a symmetric cycle R in the tope graph of a simple oriented matroid M, then for any tope T of M there exists a unique inclusion-minimal subset Q(T,R) of V(R) such that T is the sum of the topes of Q(T,R). If for…
We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$. To the best of our knowledge, this is the…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…
Variational minimization of the ground-state energy as a function of the two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions, provides a polynomial-scaling approach to studying strongly…
Gordon introduced a class of matroids $M(n)$, for prime $n\ge 2$, such that $M(n)$ is algebraically representable, but only in characteristic $n$. Lindstr\"om proved that $M(n)$ for general $n\ge 2$ is not algebraically representable if…
The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $f(\cdot)$ due to an ordering…
We introduce the notion of a quasi-matroidal class of ordered simplicial complexes: an approximation to the idea of a matroid cryptomorphism in the landscape of ordered simplicial complexes. A quasi-matroidal class contains pure shifted…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…
In this article we make several contributions of independent interest. First, we introduce the notion of stressed hyperplane of a matroid, essentially a type of cyclic flat that permits to transition from a given matroid into another with…
The concept of a matroid quotient has connections to fundamental questions in the geometry of flag varieties. In previous work, Benedetti and Knauer characterized quotients in the class of lattice path matroids (LPMs) in terms of a simple…
We give a new perspective of the relationship between simple matroids of rank 3 and pairwise balanced designs, connecting Wilson's theorems and tools with the theory of truncated boolean representable simplicial complexes. We also introduce…
A biased graph is a graph with a class of selected circles ("cycles", "circuits"), called "balanced", such that no theta subgraph contains exactly two balanced circles. A biased graph has two natural matroids, the frame matroid and the lift…