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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

15 votes

"Make all numbers equal" game

The problem is soluble for real numbers, and indeed for any tuple $(x_1, \dots, x_n)$ with $n$ even and $x_i$ real (or in any abelian group) for all $i$. (For impossibility for odd-length tuples see t …
jackdean's user avatar
  • 193
4 votes
2 answers
290 views

Is there a set of point $S \subset \mathbb R^2$ such that $|\{C: C \text{ is unit circle bou...

There are some blue points and red points on the plane such that in the boundary of every unit circle centered at one blue point there are exactly 10 red point. Can the number of blue points strictly …
jackdean's user avatar
  • 193