Related papers: A Common Generalization to Theorems on Set Systems…

Ellis and the third author showed, verifying a conjecture of Frankl, that any $3$-wise intersecting family of subsets of $\{1,2,\dots,n\}$ admitting a transitive automorphism group has cardinality $o(2^n)$, while a construction of Frankl…

We give a new proof of the Frankl-R\"odl theorem on forbidden intersections, via the probabilistic method of dependent random choice. Our method extends to codes with forbidden distances, where over large alphabets our bound is…

The main topic of this paper is various "hyperbolic" generalizations of the Edmonds-Rado theorem on the rank of intersection of two matroids. We prove several results in this direction and pose a few questions. We also give generalizations…

Let $\mathcal{A}$ be a family of subsets of a finite set. A subfamily of $\mathcal{A}$ is said to be intersecting when any two of its members contain at least one common element. We say that $\mathcal{A}$ is an Erd{\H o}s-Ko-Rado (EKR)…

Based on results by Brugall\'e and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degrees $N^{d, \delta}$ using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version of a…

The celebrated theorem of Ahlswede and Khachatrian determines the maximum size of a family of $k$-element subsets of an $n$-element set where the intersection of any two subsets has at least $r$ elements. This survey first gives a…

In this article we generalize a theorem of Benson for generalized quadrangles to strongly regular graphs and directed strongly regular graphs. The main result provides numerical restrictions on the number of fixed vertices and the number of…

We develop a new approach to approximate families of sets, complementing the existing `$\Delta$-system method' and `junta approximations method'. The approach, which we refer to as `spread approximations method', is based on the notion of…

A subset $S$ of the alternating group on $n$ points is {\it intersecting} if for any pair of permutations $\pi,\sigma$ in $S$, there is an element $i\in \{1,\dots,n\}$ such that $\pi(i)=\sigma(i)$. We prove that if $S$ is intersecting, then…

In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or…

Let $N$ be a finite set and $\mathcal{F}$, an intersection-closed family of subsets. Frankl conjectured that there always exists an element in $N$ which is contained in at most half the number of sets in $\mathcal{F}$ unless $\mathcal{F}…

A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.

Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture…

In 2000, A. Koldobsky asked whether two types of generalizations of the notion of an intersection-body, are in fact equivalent. The structures of these two types of generalized intersection-bodies have been studied by the author in…

Ochiai has previously proved that the Beilinson-Kato Euler systems for modular forms interpolate in nearly-ordinary $p$-adic families (Howard has obtained a similar result for Heegner points), based on which he was able to prove a half of…

For derived curves intersecting a family of decomposable hyperplanes in subgeneral position, we obtain an analog of Cartan-Nochka Second Main Theorem, generalizing a classical result of Fujimoto about decomposable hyperplanes in general…

Fix non-zero reals $\alpha_1,\ldots,\alpha_n$ with $n\ge 2$ and let $K$ be a non-empty open connected set in a topological vector space such that $\sum_{i\le n}\alpha_iK\subseteq K$ (which holds, in particular, if $K$ is an open convex cone…

In this paper, we extend the recent theorem of G. Heier and A. Levin [arXiv:1712.02456] on the generalization of Schmidt's subspace theorem and Cartan's Second Main Theorem in Nevanlinna theory to closed subschemes located in $l$-subgeneral…

We prove the following version of the Loebl-Komlos-Sos Conjecture: For every alpha>0 there exists a number M such that for every k>M every n-vertex graph G with at least (0.5+alpha)n vertices of degree at least (1+alpha)k contains each tree…

Three intersection theorems are proved. First, we determine the size of the largest set system, where the system of the pairwise unions is l-intersecting. Then we investigate set systems where the union of any s sets intersect the union of…