Related papers: Finite matchability under the matroidal Hall's con…

The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.\ when the goal is to decide if two common independent sets suffice or not.…

Nested matroids were introduced by Crapo in 1965 and have appeared frequently in the literature since then. A flat of a matroid $M$ is Hamiltonian if it has a spanning circuit. A matroid $M$ is nested if and only if its Hamiltonian flats…

We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either $\{x,y\}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other.…

We prove that, on a smooth, connected variety in characteristic zero admitting a rational point, local systems of geometric origin are stable under extension in the category of all local systems. As a consequence of this, we obtain a (Nori)…

In the paper, it is proved that if a finite group $G$ possesses a $\pi$-Hall subgroup for a set $\pi$ of primes, then every normal subgroup $A$ of $G$ possesses a $\pi$-Hall subgroup $H$ such that ${G=AN_G(H)}$.

The Hall--Paige conjecture asserts that a finite group has a complete mapping if and only if its Sylow subgroups are not cyclic. The conjecture is now proved, and one aim of this paper is to document the final step in the proof (for the…

We show that the following two condition measures of a full column rank matrix $A \in \mathbb{R}^{m\times n}$ are identical: the chi constant and a signed Hoffman constant. This identity is naturally suggested by the evident invariance of…

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…

In a recent paper Garber, Gavrilyuk and Magazinov proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for all five-dimensional Voronoi parallelohedra. Consequently,…

We consider the problem of determining whether the union of two infinite matroids is a matroid. We introduce a superclass of the finitary matroids, the nearly finitary matroids, and prove that the union of two nearly finitary matroids is a…

The connected components of $\mathcal{M}_{0,n}(\mathbb{R})$ are in bijection with the $(n-1)!/2$ dihedral orderings of $[n]$. They are all isomorphic. We construct monomial maps between them, and use these maps to prove a conjecture of…

If $M$ is a matroid, then a simple matroid $M'$ with the same rank as $M$ is an adjoint of $M$ if there is an inclusion-reversing embedding $\phi$ of the lattice of flats of $M$ into the lattice of flats of $M'$ such that $\phi$ maps the…

Let M be a matroid representable over a (partial) field P and B a matrix representable over a sub-partial field P' of P. We say that B confines M to P' if, whenever a P-representation matrix A of M has a submatrix B, A is a scaled…

Let $G$ be a matrix and $M(G)$ be the matroid defined by linear dependence on the set $E$ of column vectors of $G.$ Roughly speaking, a parcel is a subset of pairs $(f,g)$ of functions defined on $E$ to an Abelian group $A$ satisfying a…

As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory might extend to the infinite setting. These include base packing, base covering, and…

For fixed $r\geq 3$ and $n$ divisible by $r$, let ${\mathcal H}={\mathcal H}^r_{n,M}$ be the random $M$-edge $r$-graph on $V=\{1,\ldots ,n\}$; that is, ${\mathcal H}$ is chosen uniformly from the $M$-subsets of ${\mathcal K}:={V \choose r}$…

If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on…

We show that if the ground set of a matroid can be partitioned into $k\ge 2$ bases, then for any given subset $S$ of the ground set, there is a partition into $k$ bases such that the sizes of the intersections of the bases with $S$ may…

In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic…

We show that for an ideal $H$ in an Archimedean vector lattice $F$ the following conditions are equivalent: $\bullet$ $H$ is a projection band; $\bullet$ Any collection of mutually disjoint vectors in $H$, which is order bounded in $F$, is…