MathDB

Sequence of sets of size 4

Source: Miklos Schweitzer 2023, Problem 7

November 7, 2023

Problem Statement

Prove that there exist two subsets

D, K

of

\mathbb{N}^2

such that for any

4

-element sets

A_1, A_2

we have

|A_1 \cap A_2|=1

if and only if there exist

4

-element sets

A_3, A_4, \ldots

, such that

A_i \cap A_j=\emptyset

for all

(i, j) \in D

and

|A_i \cap A_j|=2

for all

(i, j) \in K

.

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