Related papers: Generators, extremals and bases of max cones

This note is a geometric commentary on maximum-entropy proofs. Its purpose is to illustrate the geometric structures involved in such proofs, to explain more in detail why the maximization of the entropy can be turned into the minimization…

We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of…

Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly…

Considered here is one quite general problem about description of extremal configurations maximizing the product of inner radii non-overlapping domains.

The structure of maximal faces of the cone of completely positive matrices is still not well understood in higher dimensions, mainly due to the lack of a general characterization of extreme exposed rays of the copositive cone beyond small…

We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to…

We show that in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. We also…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

Let $ SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices. Given tuples $X=(X_1, \dots, X_g) \in SM_{n_1}(\mathbb{R})^g$ and $Y=(Y_1, \dots, Y_g) \in SM_{n_2}(\mathbb{R})^g$, a matrix convex combination of $X$ and…

We determine the maximum number of edges in a $K_4$-minor-free $n$-vertex graph of girth $g$, when $g = 5$ or $g$ is even. We argue that there are many different $n$-vertex extremal graphs, if $n$ is even and $g$ is odd.

Given $n+1$ unit vectors in $\mathbf{R}^n$ or $\mathbf{C}^n,$ consider the absolute values of the determinants of the vectors taken $n$ at a time. By taking a geometric perspective, we show that the minimum of these determinants is…

We introduce the notion of an extremal subset in a geodesically complete space with curvature bounded above, i.e., a GCBA space. This is an analogue of an extremal subset in an Alexandrov space with curvature bounded below introduced by…

We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…

In this article, we establish some new combinatorial properties of cone types in Coxeter groups. Firstly, we show that for any element $x$ in a Coxeter group $W$ and root $\beta$ in its inversion set $\Phi(x)$, the set of elements $y \in W$…

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…

In the field of algebraic systems biology, the number of minimal polynomial models constructed using discretized data from an underlying system is related to the number of distinct reduced Gr\"obner bases for the ideal of the data points.…

We study the problem of finding curves of minimum pointwise-maximum arc-length derivative of curvature, here simply called curves of minimax spirality, among planar curves of fixed length with prescribed endpoints and tangents at the…

The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…

By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.

This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…