Difference between revisions of "2019 USAJMO Problems/Problem 5"
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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 integers <math>i,j</math> with <math>0\leq i,j\leq n</math>, such that: | 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 integers <math>i,j</math> with <math>0\leq i,j\leq n</math>, such that: | ||
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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 | ||
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>. | ||
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Proposed by Ricky Liu | Proposed by Ricky Liu | ||
Revision as of 18:11, 19 April 2019
Let 
be a nonnegative integer. Determine the number of ways that one can choose 
sets 
, for integers 
with 
, such that:
1. for all , the set 
has 
elements; and
2. 
whenever 
and 
.
Proposed by Ricky Liu
