Related papers: Wonderful models for toric arrangements

We study families of polynomial dynamical systems inspired by biochemical reaction networks. We focus on complex balanced mass-action systems, which have also been called toric. They are known or conjectured to enjoy very strong dynamical…

Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…

In the present paper, we study conic divisorial ideals of toric rings. We provide an idea to determine them and we give a description of the conic divisorial ideals of Hibi rings and stable set rings of perfect graphs by using this idea. We…

We propose a construction of a stable category for any pretorsion theory in a lextensive category. We prove the universal property of the stable category, that extends previous results obtained for the stable category of internal preorders…

Using log-geometry, we construct a model for the configuration category of a smooth algebraic variety. As an application, we prove the formality of certain configuration spaces.

We study the tropicalization of intersections of plane curves, under the assumption that they have the same tropicalization. We show that the set of tropical divisors that arise in this manner is a pure dimensional balanced polyhedral…

This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…

We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar…

We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.

Some projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T were constructed in [3]. In this paper we describe their integer cohomology rings by generators and relations.

In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…

We introduce notions of combinatorial blowups, building sets, and nested sets for arbitrary meet-semilattices. This gives a common abstract framework for the incidence combinatorics occurring in the context of De Concini-Procesi models of…

We prove the torsion freeness of the decomposable Orlik--Solomon algebra of a simple matroid on ground set $[n]$. In the class of hypersolvable \& non-supersolvable complex hyperplane arrangements, the torsion freeness, in a certain degree,…

Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we…

We describe the effective and the big cones of a projective symmetric variety. Moreover, we give a necessary and sufficient combinatorial criterion for the bigness of a nef divisor on a projective symmetric variety. When the variety is…

We show that a rational normal scroll can in general be set-theoretically defined by a proper subset of the 2-minors of the associated two-row matrix. This allows us to find a class of rational normal scrolls that are almost set-theoretic…

This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…

We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work on a {\em generic} representation that we illustrate on…

The existence of smooth families of Lorenz maps exhibiting all possible dynamical behavior is established and the structure of the parameter space of these families is described.