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Difference between revisions of "2019 USAJMO Problems/Problem 5"
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1. for all <math>0\leq i,j\leq n</math>, the set <math>S_{i,j}</math> has <math>i+j</math> elements; and
 
1. for all <math>0\leq i,j\leq n</math>, the set <math>S_{i,j}</math> has <math>i+j</math> elements; and
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2. <math>S_{i,j}\subseteq S_{k,l}</math> whenever <math>0\leq i\leq k\leq n</math> and <math>0\leq j\leq l\leq n</math>.
+
 
 +
2. <math>S_{i,j}\subseteq S_{k,l}</math> whenever <math>0\leq i\leq k\leq n</math> and <math>0\leq j\leq l\leq n</math>.
  
 
Proposed by Ricky Liu
 
Proposed by Ricky Liu

Revision as of 18:11, 19 April 2019

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:

1. for all $0\leq i,j\leq n$, the set $S_{i,j}$ has $i+j$ elements; and

2. $S_{i,j}\subseteq S_{k,l}$ whenever $0\leq i\leq k\leq n$ and $0\leq j\leq l\leq n$.

Proposed by Ricky Liu

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