Find $\mathcal{F}$ s.t. for each family $\mathcal{G}$ of $n$ sets each of size $n/2$, there's a $F\in \mathcal{F}$ intersecting each $G\in\mathcal{G}$

score 176 · Answer 7 · 2026-05-10 14:49:32

176

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Given $A\subset \mathbf{R}\setminus \{0\}$ with $|A| = n$, show that there is a $B\subset A$ with $|B| > n/3$ so that $(B+B)\cap B =\emptyset$

Published on 10 May 2026 - 14:49

score 280 · Answer 8 · 2026-04-14 23:04:35

280

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Help in proving this result on coloring the integers. (Lovasz Local Lemma)

Published on 14 Apr 2026 - 23:04

score 106 · Answer 9 · 2026-04-14 07:46:38

106

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Theory on showing dense global existence of pde

Published on 14 Apr 2026 - 7:46

score 1k · Answer 10 · 2026-04-13 09:09:44

1k

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Show that it is possible to color the edges of $K_n$ with at most $3 \sqrt n$ colors so that there are no monochromatic triangles.

Published on 13 Apr 2026 - 9:09

score 286 · Answer 11 · 2026-04-16 02:42:24

286

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Find the sum of the number of all continuous runs of all possible sequences with $2019$ ones and $2019$ zeros

Published on 16 Apr 2026 - 2:42

score 659 · Answer 12 · 2026-04-16 08:45:20

659

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Color each subset of $\{1,2,\ldots,n\}$ either red or blue so that each red number lies in more red subsets than blue subsets...

Published on 16 Apr 2026 - 8:45

score 614 · Answer 13 · 2026-04-09 14:10:30

614

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Combinatorics problems that can be solved more easily using probability

Published on 09 Apr 2026 - 14:10

score 219 · Answer 14 · 2026-04-15 20:37:35

219

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Let $A$ be a set of $n$ residues $\pmod{n^{2}}$. Prove that there exists a set $B$ of of $n$ residues $\pmod{n^{2}}$ ...

Published on 15 Apr 2026 - 20:37

score 119 · Answer 15 · 2026-04-16 01:47:52

119

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Zero-One Laws in Random Graph for Binomial Subgraph of Complete Bipartite graph

Published on 16 Apr 2026 - 1:47

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Find $\mathcal{F}$ s.t. for each family $\mathcal{G}$ of $n$ sets each of size $n/2$, there's a $F\in \mathcal{F}$ intersecting each $G\in\mathcal{G}$

Given $A\subset \mathbf{R}\setminus \{0\}$ with $|A| = n$, show that there is a $B\subset A$ with $|B| > n/3$ so that $(B+B)\cap B =\emptyset$

Help in proving this result on coloring the integers. (Lovasz Local Lemma)

Theory on showing dense global existence of pde

Show that it is possible to color the edges of $K_n$ with at most $3 \sqrt n$ colors so that there are no monochromatic triangles.

Find the sum of the number of all continuous runs of all possible sequences with $2019$ ones and $2019$ zeros

Color each subset of $\{1,2,\ldots,n\}$ either red or blue so that each red number lies in more red subsets than blue subsets...

Combinatorics problems that can be solved more easily using probability

Let $A$ be a set of $n$ residues $\pmod{n^{2}}$. Prove that there exists a set $B$ of of $n$ residues $\pmod{n^{2}}$ ...

Zero-One Laws in Random Graph for Binomial Subgraph of Complete Bipartite graph

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