Related papers: Adjoints of Matroids
We study point-line configurations, their minimal matroids, and their associated circuit varieties. We present an algorithm for identifying the minimal matroids of these configurations with respect to dependency order, or equivalently, the…
For a symplectic vector space $V$, a projective subvariety $Z \subset {\bf P} V$ is a Legendrian variety if its affine cone $\widehat{Z} \subset V$ is Lagrangian. In addition to the classical examples of subadjoint varieties associated to…
In this paper, first steps are taken towards characterising lattices of cyclic flats $\mathcal{Z}(M)$ that belong to matroids $M$ that can be represented over a prescribed finite field $\mathbb{F}_q$. Two natural maps from $\mathcal{Z}(M)$…
There are many contexts in algebraic geometry, algebraic topology, and homological algebra where one encounters a functor that has both a left and right adjoint, with the right adjoint being isomorphic to a shift of the left adjoint…
We explore novel connections between antimatroids and matchings in bipartite graphs. In particular, we prove that a combinatorial structure induced by stable matchings or maximum-weight matchings is an antimatroid. Moreover, we demonstrate…
This paper studies systems of polynomial equations that provide information about orientability of matroids. First, we study systems of linear equations over GF(2), originally alluded to by Bland and Jensen in their seminal paper on weak…
A matroid $N$ is said to be triangle-rounded in a class of matroids $\mathcal{M}$ if each $3$-connected matroid $M\in \mathcal{M}$ with a triangle $T$ and an $N$-minor has an $N$-minor with $T$ as triangle. Reid gave a result useful to…
We prove that if a unitary representation of a connected Lie group has the property that no nonozero vector is fixed by any nontrival normal connected subgroup, then the matrix coefficients decay to zero at Adjoint-infinity.
A recent line of research has concentrated on exploring the links between analytic and combinatorial theories of submodularity, uncovering several key connections between them. In this context, Lov\'asz initiated the study of matroids from…
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural…
Let A be a connected hereditary artin algebra. We show that the set of functorially finite torsion classes of A-modules is a lattice if and only if A is either representation-finite (thus a Dynkin algebra) or A has only two simple modules.…
For a matroid $M$, an element $e$ such that both $M\backslash e$ and $M/e$ are regular is called a regular element of $M$. We determine completely the structure of non-regular matroids with at least two regular elements. Besides four small…
A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miyano, and Ueno states that a matroid M is cyclically…
In this paper, we investigate the relation between a $q$-matroid and its associated matroid called the projectivization matroid. The latter arises by projectivizing the groundspace of the $q$-matroid and considering the projective space as…
In this paper we give a combinatorial view on the adjunction theory of toric varieties. Inspired by classical adjunction theory of polarized algebraic varieties we define two convex-geometric notions: the Q-codegree and the nef value of a…
A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex…
Targets are matroids that arise from a nested sequence of flats in a projective geometry. This class of matroids was introduced by Nelson and Nomoto, who found the forbidden induced restrictions for binary targets. This paper generalizes…
The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An…
We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…
The authors [3] proved that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and described its monolith. Here we prove that the endomorphism semiring of a commutative inverse semigroup with at least…