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18 hours ago · Let H n ( 3 ) be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, called wicket, is formed by three rows and two columns of a 3 × 3 point matrix. We describe two linear hypergraphs that if we forbid either of them in H n ( 3 ), then the hypergraph is sparse, i.e. the number of its edges is ...
5 days ago · Pannwitz and Hopf [ 4] proved that the largest distance between points of 𝐴 A italic_A can occur at most 𝑛 n italic_n times, but it remains unknown whether a second such distance must occur. Erdős and Pach believe that such a distance exists. Another popular distance problem of Erdős mentioned alongside the distinct distance problem [ 2 ...
6 days ago · Erdős in 1992. Paul Erdős (1913–1996) was a Hungarian mathematician. He considered mathematics to be a social activity and often collaborated on his papers, having 511 joint authors, many of whom also have their own collaborators. The Erdős number measures the "collaborative distance" between an author and Erdős. Thus, his direct co ...
5 days ago · An elementary proof of Bertrand's postulate on the existence of a prime in any interval of the form [,], one of the first results of Paul Erdős, was based on the divisibility properties of factorials.
18 hours ago · Abstract Arc-Disjoint Cycle Packing is a classical NP-complete problem and we study it from two perspectives: (1) by restricting the cycles in the packing to be of a fixed length, and (2) by restri...
2 days ago · We will discuss recent work on this conjecture (joint with Alex Scott and Paul Seymour, and partly with Matija Bucić), which includes the loglog improvement over the general bound of Erdős and Hajnal, Rödl’s theorem and the polynomial Rödl property, and the method of iterative sparsification with application to prime graphs and graphs of ...
6 days ago · Will in the World is a Pulitzer Prize finalist and a New York Times Bestseller. Greenblatt is heralded by critics as one of the world’s best interpreters of the Bard’s plays, and he is recognized as one of the most acclaimed Shakespeare scholars alive.
