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Results tagged with co.combinatorics
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user 143715
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
16
votes
1
answer
798
views
Corners theorem in finite fields
The corners theorem of Ajtai and Szemerédi states that if $A\subseteq[N]^2$ is corner-free, i.e. there are no $x,y,h\in\mathbb{N}$ with all of $(x,y),(x+h,y),(x,y+h)$ in $A$, then $|A|=o(N^2)$. The st …
- 181
2
votes
1
answer
120
views
Computation of cyclic van der Waerden numbers
Van der Waerden's theorem gives us a finite number $W(k,r)$ defined as the smallest positive integer $N$ such that for any $n\geq N$, any $r$-coloring of $[n]=\{1,\dots,n\}$ admits a monochromatic $k$ …
- 181