A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that ...

In this paper we analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a discrete lion and man game with an $\varepsilon$-capture ...

Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic ...

The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. ...

In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of ...

Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and ...

A pair of non-empty subsets $(W,W')$ in an abelian group $G$ is a complement pair if $W+W'=G$. $W'$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \forall \,w'\in W'$. In general, given an arbitrary subset ...

Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. ...

Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such ...

Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number ...