We introduce certain torus-equivariant classes on permutohedral varieties which we call
“tautological classes of matroids” as a new geometric framework for studying matroids …

A variety of probabilistic notions of network reliability of graphs and digraphs have been
proposed and studied since the early 1950s. Although grounded in the engineering and …

We introduce the conormal fan of a matroid $\operatorname {M} $, which is a Lagrangian
analog of the Bergman fan of $\operatorname {M} $. We use the conormal fan to give a …

In this paper we survey geometric and arithmetic techniques to study the cohomology of
semiprojective hyperkaehler manifolds including toric hyperkaehler varieties, Nakajima …

Рассматривается один из методов анализа и синтеза структур сетей связи,
основанный на наиболее простом подходе к вопросу расчета вероятности связности …

Matroids are combinatorial abstractions of independence, a ubiquitous notion that pervades
many branches of mathematics. June Huh and his collaborators recently made spectacular …

arXiv:1302.5852v3 [math.AG] 31 May 2014 Page 1 arXiv:1302.5852v3 [math.AG] 31 May
2014 Positivity of Chern classes of Schubert cells and varieties June Huh Abstract We show …

We explore the relationship between a certain “abelian duality” property of spaces and the
propagation properties of their cohomology jump loci. To that end, we develop the analogy …

In this paper we assume that a network is a probabilistic graph where the vertices do not fail
while the edges do, being operational independently with probability p. The two most …

One of the major open questions in matroid theory asks whether the-vector of the broken
circuit complex of a matroid satisfies the following inequalities: h 0≤ h 1≤⋯≤ h⌊ s/2⌋ and …