We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suit...

Intersection results for families of H-convex sets in H-spaces are given. These extend known results concerning families of convex sets in topological vector spaces, such as the Berge-Klee intersection theorem and a previous result of the author. MSC 2000. 52A01, 14E20.

“ This paper defines reduction on derivations (cut-elimination) in the Strict Intersection Type Assignment System of [1] and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability of terms, using intersection types. ”

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

Using a result of Orlov on Fourier-Mukai transforms we construct a homomorphism from the automorphism group of the derived category to the automorphism group of the Mukai lattice on a K3 surface. Applying Mukai's moduli space construction we show that this homomorphism is surjective up to index 2. Let X be a projective K3 surface over the eld C. Its singular cohomology H∗(X,Z) is free of rank 2...

The tensor product $$R\otimes S$$ of two algebras can have its multiplication deformed by a bicharacter to yield twisted ^t . We completely describe the Hochschild cohomology in terms components R and S, including full Gerstenhaber algebra structure. This description generalizes result Bergh Oppermann. A number interesting classes noncommutative arise as products, sometimes non-obvious ways. ma...

In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for graphs with small intersection number and random intersection graphs (a model in which each one of m labels is chosen independently with probability p by each ...

Reny and Wooders (1998) showed that there is some point in the intersection of sets in Shapley’s (1973) generalization of the Knaster-Kuratowski-Mazurkiwicz Theorem with the property that the collection of all sets containing that point is partnered as well as balanced. We provide a further extension by showing that the collection of all such sets can be chosen to be strictly balanced, implying...

In simply typed λ-calculus with one ground type the following theorem due to Loader holds. (i) Given the full model F over a finite set, the question whether some element f ∈ F is λ-definable is undecidable. In the λ-calculus with intersection types based on countably many atoms, the following is proved by Urzyczyn. (ii) It is undecidable whether a type is inhabited. Both statements are major r...

Let X = {1,. . ., n) and Í" = {1,..., k), k < n. Let C(n, k) be the subsets of X which intersect Y, ordered by inclusion. Lih showed that C(n, k) has the Sperner property. Here it is shown that C(n, k) has several stronger properties. A nested chain decomposition is constructed for C(n, k) by bracketing. C(n, k) is shown to have the LYM property. A more general class of collections of subsets i...