The 11-element case of Frankl's conjecture.
The additive complements of primes and Goldbach's problem
We extend two results of Ruzsa and Vu on the additive complements of primes.
The automorphism group of the random lattice is not amenable
We prove that the automorphism group of the random lattice is not amenable, and we identify the universal minimal flow for the automorphism group of the random distributive lattice.
The integer sequence A002620 and upper antagonistic functions.
The intersection structure of -intersecting families.
The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic
A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and contains...
The minimum number of monotone subsequences.
The structure of maximal zero-sum free sequences
The structure of maximum subsets of with no solutions to .
The Turán density of the hypergraph .
The Turán problem for hypergraphs on fixed size.
The wildcard set's size in the density Hales-Jewett theorem.
Three-and-more set theorems
In this paper we generalize classical 3-set theorem related to stable partitions of arbitrary mappings due to Erdős-de Bruijn, Katětov and Kasteleyn. We consider a structural generalization of this result to partitions preserving sets of inequalities and characterize all finite sets of such inequalities which can be preserved by a “small” coloring. These results are also related to graph homomorphisms and (oriented) colorings.
Thue-like sequences and rainbow arithmetic progressions.
Towards a Katona type proof for the 2-intersecting Erdős-Ko-Rado theorem.
Traces of uniform families of sets.
Traces without maximal chains.
Transversals of rectangular arrays.
Triangle free sets and arithmetic progressions---two Pisier type problems.
Triangle-intersecting families of graphs