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erdős #83

← #82 · #84 → (packet.json; erdosproblems.com)

Suppose that we have a family $F$ of subsets of $[4 n]$ such that $∣ A ∣ = 2 n$ for all $A \in F$ and for every $A, B \in F$ we have $∣ A \cap B ∣ \geq 2$ . Then $∣ F ∣ \leq \frac{1}{2} ((2 n 4 n) - (n 2 n)^{2}) .$

Worked, still open.

combinatorics · solved · prize $500 · 0 attempts

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A071799 — Number of lattice paths in the lattice [0..2n] X [0..2n] which do not pass through the point (n,n).2,34,524,7970,121252,1850380,28337976,435443490,6711230900,103711749284,1606464657096,24935144010764,387746052588104,603 A387635 — a(n) = Sum_{k=0..n-1} binomial(2*n, k)^2.0,1,17,262,3985,60626,925190,14168988,217721745,3355615450,51855874642,803232328548,12467572005382,193873026294052,30196

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solved

finding.noted · reviewer:will-blair · 1 day

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