Related papers: The Interplay between Additive and Multiplicative …
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects $T$ in cluster categories; we call such an algebra cluster-concealed in case $T$ is obtained from a…
The study of theory combination in Satisfiability Modulo Theories (SMT) involves various model theoretic properties (e.g., stable infiniteness, smoothness, etc.). We show that such properties can be partly captured by the natural density of…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…
We introduce a connection between Newhouse thickness and patterns through a variant of Schmidt's game introduced by Broderick, Fishman and Simmons. This yields an explicit, robust and checkable condition that ensures the presence of…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
The notion of density of a finite set is introduced. We prove a general theorem of set theory which refines the Gibbs, Bose--Einstein, and Pareto distributions as well as the Zipf law.
Since their introduction by Furstenberg in 1967, joinings have proved a very powerful tool in ergodic theory. We present here some aspects of the use of joinings in the study of measurable dynamical systems, emphasizing on - the links…
We extend the theory of fields/distributions developed the paper "A Feigin-Frenkel theorem with n singularities" to a general base scheme. In order to do so we introduce suitable notions of topological sheaves on schemes and study their…
Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much…
We introduce a powerful connection between Ehrhart theory and additive number theory, and use it to produce infinitely many new classes of inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope. This greatly…
We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…
The concept of centrally symmetric configurations of integer matrices is introduced. We study the problem when the toric ring of a centrally symmetric configuration is normal as well as is Gorenstein. In addition, Gr\"obner bases of toric…
Large sets of combinatorial designs has always been a fascinating topic in design theory. These designs form a partition of the whole space into combinatorial designs with the same parameters. In particular, a large set of block designs,…
Furstenberg has associated to every topological group $G$ a universal boundary $\partial(G)$. If we consider in addition a subgroup $H<G$, the relative notion of $(G,H)$-boundaries admits again a maximal object $\partial(G,H)$. In the case…
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…