The theory of limits of discrete combinatorial objects has been thriving for the last decade or
so. The syntactic, algebraic approach to the subject is popularly known as' flag algebras' …

Let C (n) denote the maximum number of induced copies of 5-cycles in graphs on n vertices.
For n large enough, we show that C (n)= a⋅ b⋅ c⋅ d⋅ e+ C (a)+ C (b)+ C (c)+ C (d)+ C (e) …

We investigate when limits of graphs (graphons) and permutations (permutons) are uniquely
determined by finitely many densities of their substructures, ie, when they are finitely forcible …

The nn‐dimensional hypercube Q n Q_n is a graph with vertex set 0, 1 n {0,1\}^n such that
there is an edge between two vertices if and only if they differ in exactly one coordinate. For …

For the most part, this article is a survey of concrete results in extremal combinatorics
obtained with the method of flag algebras. But our survey is also preceded, interleaved and …

In this paper we describe a number of extensions to Razborov's semidefinite flag algebra
method. We will begin by showing how to apply the method to significantly improve the …

We show that for every sufficiently large n, the number of monotone subsequences of length
four in a permutation on n points is at least\begin {equation*}\binom {\lfloor …

Erdős and Sós proposed the problem of determining the maximum number F (n) of rainbow
triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F (n)= F …

Increasing attention is being paid to the study of families of subsets of an n-set that contain
no subposet P. Especially, we are interested in such families of maximum size given P and …

A graph is cubical if it is a subgraph of a hypercube. For a cubical graph H and a hypercube
Q n, ex (Q n, H) is the largest number of edges in an H-free subgraph of Q n. If ex (Q n, H) is …