相关论文: The Free product of Matroids
Let $R$ be a finite ring and let $M, N$ be two finite left $R$-modules. We present two distinct deterministic algorithms that decide in polynomial time whether or not $M$ and $N$ are isomorphic, and if they are, exhibit an isomorphism. As…
We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In \S\ref{Section6}, we…
We prove, by means of an exact structural description, that every simple triangle-free binary matroid $M$ with $|M| > \tfrac{33}{128}2^{r(M)}$ has critical number at most $2$.
We study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular $2\times 2$ matrices with rational entries when the products are restricted to certain bounded languages.
Let $M$ be a matroid. We study the expansions of $M$ mainly to see how the combinatorial properties of $M$ and its expansions are related to each other. It is shown that $M$ is a graphic, binary or a transversal matroid if and only if an…
We introduce the notion of a quasi-matroidal class of ordered simplicial complexes: an approximation to the idea of a matroid cryptomorphism in the landscape of ordered simplicial complexes. A quasi-matroidal class contains pure shifted…
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…
Associated to a finite graph $X$ is its quantum automorphism group $G(X)$. We prove a formula of type $G(X*Y)=G(X)*_wG(Y)$, where $*_w$ is a free wreath product. Then we discuss representation theory of free wreath products, with the…
We study $N$-ary non-commutative notions of independence, which are given by trees and which generalize free, Boolean, and monotone independence. For every rooted subtree $\mathcal{T}$ of the $N$-regular tree, we define the…
Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green function of the corresponding random walk. It is known from the work of W. Woess that when a finitely supported…
Free theorems are a popular tool in reasoning about parametrically polymorphic code. They are also of instructive use in teaching. Their derivation, though, can be tedious, as it involves unfolding a lot of definitions, then hoping to be…
A matroid is a combinatorial structure that captures and generalizes the algebraic concept of linear independence under a broader and more abstract framework. Matroids are closely related with many other topics in discrete mathematics, such…
Let $k$ be a field of characteristic different from $2$ and let $G$ be a nonabelian residually torsion-free nilpotent group. It is known that $G$ is an orderable group. Let $k(G)$ denote the subdivision ring of the Malcev-Neumann series…
In recent years, combinatorial reconfiguration problems have attracted great attention due to their connection to various topics such as optimization, counting, enumeration, or sampling. One of the most intriguing open questions concerns…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
We consider the two-matrix model with potentials whose derivative are arbitrary rational function of fixed pole structure and the support of the spectra of the matrices are union of intervals (hard-edges). We derive an explicit formula for…
We give an explicit description, via analytic subordination, of free multiplicative convolution of operator-valued distributions. In particular, the subordination function is obtained from an iteration process. This algorithm is easily…
Inspired by a recent result of Brakensiek et al. that symmetric tensor matroids and rigidity matroids are linked by matroid duality, we define abstract symmetric tensor matroids as a dual concept to abstract rigidity matroids and establish…
The first non-trivial case of Hadwiger's conjecture for oriented matroids reads as follows. If $\mathcal{O}$ is an $M(K_4)$-free oriented matroid, then $\mathcal{O}$ admits a NZ $3$-coflow, i.e., it is $3$-colourable in the sense of…
We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on…