## References

SHOWING 1-10 OF 16 REFERENCES

A New Lower Bound Based on Gromov’s Method of Selecting Heavily Covered Points

- MathematicsDiscret. Comput. Geom.
- 2012

Using methods from extremal combinatorics, one of the quantities appearing in Gromov’s approach is improved and thereby provided a new stronger lower bound on cd for arbitrary d, which is improved from 0.06332 to more than 0.07480.

Almost similar configurations

- Mathematics
- 2018

Let $h(n)$ denote the maximum number of triangles with angles between $59^\circ$ and $61^\circ$ in any $n$-element planar set. Our main result is an exact formula for $h(n)$. We also prove $h(n)=…

Maximum density of induced 5-cycle is achieved by an iterated blow-up of 5-cycle

- MathematicsEur. J. Comb.
- 2016

Improving bounds on packing densities of 4-point permutations

- Mathematics, Computer ScienceDiscret. Math. Theor. Comput. Sci.
- 2017

The main tool for the upper bounds is the framework of flag algebras introduced by Razborov in 2007, which provides new upper bounds for several small permutations of length at least five and a fairly complete picture of all 4-point packing densities.

Flag algebras

- MathematicsJournal of Symbolic Logic
- 2007

The first application of a formal calculus that captures many standard arguments in the area of asymptotic extremal combinatorics is given by presenting a new simple proof of a result by Fisher about the minimal possible density of triangles in a graph with given edge density.

On Ramsey Like Theorems , Problems and Results

- Mathematics
- 2005

(1) n → (k1, . . . , k`)` means that if we split the r-tuples of a set, S, |S| = n into ` classes, than for some i, 1 ≤ i ≤ ` there is a subset Si ⊆ S, |Si| ≥ ki all of whose r-tuples are in the i-th…

Minimum Number of Monotone Subsequences of Length 4 in Permutations

- MathematicsCombinatorics, Probability and Computing
- 2014

It is shown that all the extremal colourings must contain monochromatic K4 only in one of the two colours, and this translates back to permutations, where all the monotone subsequences of length four are all either increasing, or decreasing only.

Applications of the Semi-Definite Method to the Turán Density Problem for 3-Graphs

- MathematicsCombinatorics, Probability and Computing
- 2012

Flagmatic, an implementation of Razborov's semi-definite method, is made publicly available, and several new constructions, conjectures and bounds for Turán densities of 3-graphs which should be of interest to researchers in the area are given.