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2019 USAJMO Problems/Problem 5

Revision as of 19:11, 19 April 2019 by Kevinmathz (talk | contribs) (Created page with "Let <math>n</math> be a nonnegative integer. Determine the number of ways that one can choose <math>(n+1)^2</math> sets <math>S_{i,j}\subseteq\{1,2,\ldots,2n\}</math>, for int...")
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Let $n$ be a nonnegative integer. Determine the number of ways that one can choose $(n+1)^2$ sets $S_{i,j}\subseteq\{1,2,\ldots,2n\}$, for integers $i,j$ with $0\leq i,j\leq n$, such that: [list] [*] for all $0\leq i,j\leq n$, the set $S_{i,j}$ has $i+j$ elements; and [*] $S_{i,j}\subseteq S_{k,l}$ whenever $0\leq i\leq k\leq n$ and $0\leq j\leq l\leq n$. [/list]

[i]Proposed by Ricky Liu[/i]

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