Related papers: Character tables are ideal Perron similarities

A perfect Euler cuboid is a rectangular parallelepiped with integer edges, with integer face diagonals, and with integer space diagonal as well. Finding such parallelepipeds or proving their non-existence is an old unsolved mathematical…

We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal of an ample groupoid algebra over a field is an intersection of kernels of induced representations from isotropy groups, with a much shorter proof,…

Higher-dimensional analogs of the predictable degree property and column reducedness are defined, and it is proved that the two properties are equivalent. It is shown that every multidimensional convolutional code has, what is called, a…

A set $\mathcal{S}$ of points in $\mathbb{R}^n$ is called a rationally parameterisable hypersurface if $\mathcal{S}=\{\boldsymbol{\sigma}(\mathbf{t}): \mathbf{t} \in D\}$, where $\boldsymbol{\sigma}: \mathbb{R}^{n-1} \rightarrow…

In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…

We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes we conclude that every such algebra is normal and Cohen-Macaulay, and give an interpretation of its…

A model for a finite group is a set of linear characters of subgroups that can be induced to obtain every irreducible character exactly once. A perfect model for a finite Coxeter group is a model in which the relevant subgroups are the…

The Dehn property for a complex is that every non-trivial disk diagram has spurs or shells. It implies a linear isoperimetric inequality. It has been conjectured that the same is true of a more general property which also allows cutcells.…

If I is a nilpotent ideal in a $\mathbb{Q}$-algebra $A$, Goodwillie defined two isomorphisms from $K_*(A,I)$ to negative cyclic homology, $HN_*(A,I)$. One is the relative version of the absolute Chern character, and the other is defined…

We classify thick tensor ideals of finite objects in the category of rational torus-equivariant spectra, showing that they are completely determined by geometric isotropy. This is essentially equivalent to showing that the Balmer spectrum…

We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feasible region}. We show that this feasible region is a…

If A is a nonnegative matrix whose associated directed graph is strongly connected, the Perron-Frobenius theorem asserts that A has an eigenvector in the positive cone, (R^+)^n. We associate a directed graph to any homogeneous, monotone…

Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as planar, 3-regular graphs with facets…

Combinatorial neural codes are $0/1$ vectors that are used to model the co-firing patterns of a set of place cells in the brain. One wide-open problem in this area is to determine when a given code can be algorithmically drawn in the plane…

A ``hyperideal circle pattern'' in $S^2$ is a finite family of oriented circles, similar to the ``usual'' circle patterns but such that the closed disks bounded by the circles do not cover the whole sphere. Hyperideal circle patterns are…

Given an ample action of an inverse semigroup on a locally compact and Hausdorff topological space, we study the ideal structure of the crossed product algebra associated with it. By developing a theory of induced ideals, we manage to prove…

Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a…

Let $A$ be a commutative Noetherian local ring with maximal ideal $\mathfrak{m}$, and let $I$ be an ideal. The fiber cone is then an image of the polynomial ring over the residue field $A/\mathfrak{m}$. The kernel of this map is called the…

It is well-known that if R is a domain with finite character, each locally principal nonzero ideal of R is invertible. We address the problem of understanding when the converse is true and survey some recent results.

An orbit polytope is the convex hull of an orbit under a finite group $G \leq \operatorname{GL}(d,\mathbb{R})$. We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense…