Related papers: Matroidal representations of low rank

This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…

If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In…

A representation $\Phi: G \to \mathrm{GL}_n(\mathbb{F})$ of a finite group $G$ is called unisingular if the matrix $\Phi(g)$ admits $1$ as an eigenvalue for any $g\in G$. In this paper, we determine all the complex irreducible unisingular…

A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads…

We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave…

Suppose that $f$ is a homomorphism from the mapping class group $\mathcal{M}(N_{g,n})$ of a nonorientable surface of genus $g$ with $n$ boundary components, to $\mathrm{GL}(m,\mathbb{C})$. We prove that if $g\ge 5$, $n\le 1$ and $m\le g-2$,…

Let A be a complex abelian variety and G its Mumford--Tate group. Supposing that the simple abelian subvarieties of A are pairwise non-isogenous, we find a lower bound for the rank of G, which is a little less than log_2 dim A. If we…

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…

If G and H are finitely generated, residually nilpotent metabelian groups, H is termed para-G if there is a homomorphism of G into H which induces an isomorphism between the corresponding terms of their lower central quotient groups. We…

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…

We introduce the rank-nullity ring of a matroid $M$, which is a subring of the Chow ring of the permutahedral toric variety. This subring contains the tautological Chern classes of $M$, a fact we deduce from a highly symmetric formula for…

W.H.~Mills has determined, for a finitely generated abelian group $G$, the regular subgroups $N \cong G$ of $S(G)$, the group of permutations on the set $G$, which have the same holomorph of $G$, that is, such that $N_{S(G)}(N) =…

q-Matroids form the q-analogue of classical matroids. In this paper we introduce various types of maps between q-matroids. These maps are not necessarily linear, but they map subspaces to subspaces and respect the q-matroid structure in…

Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups:…

In the present paper, we provide a cohomology group as a categorification of the characteristic polynomial of matroids. The construction depends on the ``quasi-representation'' of a matroid. For a certain choice of the quasi-representation,…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

In this paper, we associate Galois representations to globally generic cuspidal automorphic representations on GSp(4), over a totally real field F, which are Steinberg at some finite place. This association is compatible with the local…

We investigate the asymptotic behavior of entropy polymatroids associated with algebraic matroids over finite fields. Given an algebraic matroid ${\sf M}:=(\mathcal{E},r)$ and the irreducible variety $V$ associated with ${\sf M}$, we…

We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $H\le…

A G-gain graph is a graph whose oriented edges are labeled invertibly from a group G. Zaslavsky proposed two matroids of G-gain graphs, called frame matroids and lift matroids, and investigated linear representations of them. Each matroid…