Question

Partitions with maximal length

score 94 · Answer 1 · 2023-03-26 14:34:27

94

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Partitions with maximal length

Published on 26 Mar 2023 - 14:34

score 329 · Answer 2 · 2026-03-25 17:33:50

329

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Let $S_1, S_2, \dots , S_m$ be distinct subsets of $\{1, 2, \dots , n\}$ such that $|S_i \cap S_j | = 1$ for all $i \ne j$. Prove that $m \le n$.

Published on 25 Mar 2026 - 17:33

score 53 · Answer 3 · 2026-03-25 10:57:15

53

Views

Prove that $A_i$ has at least $1$ member that is not colored.

Published on 25 Mar 2026 - 10:57

score 91 · Answer 4 · 2023-04-06 17:11:21

91

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Building a puzzle game - how to calculate total of combination sets once "invalid" results are excluded?

Published on 06 Apr 2023 - 17:11

score 67 · Answer 5 · 2026-03-26 14:20:56

67

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Triangle-free graphs on a set $V$ of $n$ labeled vertices

Published on 26 Mar 2026 - 14:20

score 42 · Answer 6 · 2026-03-26 14:19:42

42

Views

Proving existence of $d$-regular subgraph

Published on 26 Mar 2026 - 14:19

score 64 · Answer 7 · 2026-03-26 16:05:56

64

Views

Lower bound for the maximal complete subgraphs with all edges of the same color, for a complete graph

Published on 26 Mar 2026 - 16:05

score 24 · Answer 8 · 2023-04-17 15:15:26

24

Views

Prove: Every collection of r subsets each with atleast $|X|(1-\frac{1}{r})$ points of X has a non empty intersection.

Published on 17 Apr 2023 - 15:15

score 85 · Answer 9 · 2026-03-25 17:33:50

85

Views

A family of subsets each of size $r$ must witness decent size of intersection for some two members.

Published on 25 Mar 2026 - 17:33

score 493 · Answer 10 · 2023-04-29 03:36:02

493

Views

Find the maximum number of elements in the set $M$ such that no two elements have a difference of $5$ or $8$

Published on 29 Apr 2023 - 3:36

score 78 · Answer 11 · 2026-03-25 17:32:44

78

Views

Existence of a Hadamard-like matrix

Published on 25 Mar 2026 - 17:32

score 44 · Answer 12 · 2023-05-03 01:54:18

44

Views

Collection of hyperplanes covering $\{ 0,1,2 \}^d$

Published on 03 May 2023 - 1:54

score 82 · Answer 13 · 2023-05-09 22:41:13

82

Views

Number of subsets with no pairwise intersection of cardinality 2?

Published on 09 May 2023 - 22:41

score 33 · Answer 14 · 2023-05-22 20:35:15

33

Views

Bounding the size of set systems if the parity of intersection sizes are fixed.

Published on 22 May 2023 - 20:35

score 12 · Answer 15 · 2026-02-27 14:31:59

12

Views

Getting a partite minimum co-degree in a $k$-partite $k$-uniform hypergraph

Published on 27 Feb 2026 - 14:31

List Question

Partitions with maximal length

Let $S_1, S_2, \dots , S_m$ be distinct subsets of $\{1, 2, \dots , n\}$ such that $|S_i \cap S_j | = 1$ for all $i \ne j$. Prove that $m \le n$.

Prove that $A_i$ has at least $1$ member that is not colored.

Building a puzzle game - how to calculate total of combination sets once "invalid" results are excluded?

Triangle-free graphs on a set $V$ of $n$ labeled vertices

Proving existence of $d$-regular subgraph

Lower bound for the maximal complete subgraphs with all edges of the same color, for a complete graph

Prove: Every collection of r subsets each with atleast $|X|(1-\frac{1}{r})$ points of X has a non empty intersection.

A family of subsets each of size $r$ must witness decent size of intersection for some two members.

Find the maximum number of elements in the set $M$ such that no two elements have a difference of $5$ or $8$

Existence of a Hadamard-like matrix

Collection of hyperplanes covering $\{ 0,1,2 \}^d$

Number of subsets with no pairwise intersection of cardinality 2?

Bounding the size of set systems if the parity of intersection sizes are fixed.

Getting a partite minimum co-degree in a $k$-partite $k$-uniform hypergraph

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