Related papers: Linear independences of maps associated to partiti…
Tutte's celebrated barycentric embedding theorem describes a natural way to build straight-line embeddings (crossing-free drawings) of a (3-connected) planar graph: map the vertices of the outer face to the vertices of a convex polygon, and…
In this paper, we are interested in sequences of q-tuple of N-by-N random matrices having a strong limiting distribution (i.e. given any non-commutative polynomial in the matrices and their conjugate transpose, its normalized trace and its…
Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…
We study four (families of) sets of algebraic integers of degree less than or equal to three. Apart from being simply defined, we show that they share two distinctive characteristics: almost uniformity and arithmetical independence. Here,…
Relying on the theory of agrarian invariants introduced in previous work, we solve a conjecture of Friedl-Tillmann: we show that the marked polytopes they constructed for two-generator one-relator groups with nice presentations are…
A new result of G. Cz\'edli states that for an ordered set $P$ with at least two elements and a group $G$, there exists a bounded lattice $L$ such that the ordered set of principal congruences of $L$ is isomorphic to $P$ and the…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
We study topological versions of an independent set in an abelian group and a linearly independent set in a vector space, a {\em topologically independent set} in a topological group and a {\em topologically linearly independent set} in a…
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…
In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our…
We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…
W.Specht (1940) proved that two $n\times n$ complex matrices $A$ and $B$ are unitarily similar if and only if $\operatorname{trace} w(A,A^{\ast}) = \operatorname{trace} w(B,B^{\ast})$ for every word $w(x,y)$ in two noncommuting variables.…
We give a simple direct proof of the Jamiolkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accesible for physicists than others found in the literature and provides a…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
The configuration of a matroid $M$ is the abstract lattice of cyclic flats (flats that are unions of circuits) where we record the size and rank of each cyclic flat, but not the set. One can compute the Tutte polynomial of $M$, and stronger…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
We introduce the notion of identity component of a compact quantum group and that of total disconnectedness. As a drawback of the generalized Burnside problem, we note that totally disconnected compact matrix quantum groups may fail to be…
Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement…