Combinatorial problems in finding the number of subsets of $S_n$
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For $A subset mathbb{R}$, let $A'={a+1|a in A}$. Let $S_n={1;2;3;...;n}$. How many subsets $A$ of $S_n$ satisfying $A cup A' = S_n$?
I'm trying to solve this problem by using bijection or constructing a sequence but still struggling. Please help me with this.
combinatorics
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
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add a comment |
$begingroup$
For $A subset mathbb{R}$, let $A'={a+1|a in A}$. Let $S_n={1;2;3;...;n}$. How many subsets $A$ of $S_n$ satisfying $A cup A' = S_n$?
I'm trying to solve this problem by using bijection or constructing a sequence but still struggling. Please help me with this.
combinatorics
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
$endgroup$
$begingroup$
Have you tried making examples for small $n?$
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– saulspatz
Dec 8 '18 at 15:45
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Hint: You can find a recurrence for your answer by conditioning on whether or not $nin A$.
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– Mike Earnest
Dec 8 '18 at 17:47
1
$begingroup$
See math.stackexchange.com/questions/261326/….
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– Anubhab Ghosal
Dec 8 '18 at 18:23
add a comment |
$begingroup$
For $A subset mathbb{R}$, let $A'={a+1|a in A}$. Let $S_n={1;2;3;...;n}$. How many subsets $A$ of $S_n$ satisfying $A cup A' = S_n$?
I'm trying to solve this problem by using bijection or constructing a sequence but still struggling. Please help me with this.
combinatorics
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
$endgroup$
For $A subset mathbb{R}$, let $A'={a+1|a in A}$. Let $S_n={1;2;3;...;n}$. How many subsets $A$ of $S_n$ satisfying $A cup A' = S_n$?
I'm trying to solve this problem by using bijection or constructing a sequence but still struggling. Please help me with this.
combinatorics
combinatorics
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
asked Dec 8 '18 at 15:19
Martin TrMartin Tr
1217
1217
$begingroup$
Have you tried making examples for small $n?$
$endgroup$
– saulspatz
Dec 8 '18 at 15:45
$begingroup$
Hint: You can find a recurrence for your answer by conditioning on whether or not $nin A$.
$endgroup$
– Mike Earnest
Dec 8 '18 at 17:47
1
$begingroup$
See math.stackexchange.com/questions/261326/….
$endgroup$
– Anubhab Ghosal
Dec 8 '18 at 18:23
add a comment |
$begingroup$
Have you tried making examples for small $n?$
$endgroup$
– saulspatz
Dec 8 '18 at 15:45
$begingroup$
Hint: You can find a recurrence for your answer by conditioning on whether or not $nin A$.
$endgroup$
– Mike Earnest
Dec 8 '18 at 17:47
1
$begingroup$
See math.stackexchange.com/questions/261326/….
$endgroup$
– Anubhab Ghosal
Dec 8 '18 at 18:23
$begingroup$
Have you tried making examples for small $n?$
$endgroup$
– saulspatz
Dec 8 '18 at 15:45
$begingroup$
Have you tried making examples for small $n?$
$endgroup$
– saulspatz
Dec 8 '18 at 15:45
$begingroup$
Hint: You can find a recurrence for your answer by conditioning on whether or not $nin A$.
$endgroup$
– Mike Earnest
Dec 8 '18 at 17:47
$begingroup$
Hint: You can find a recurrence for your answer by conditioning on whether or not $nin A$.
$endgroup$
– Mike Earnest
Dec 8 '18 at 17:47
1
1
$begingroup$
See math.stackexchange.com/questions/261326/….
$endgroup$
– Anubhab Ghosal
Dec 8 '18 at 18:23
$begingroup$
See math.stackexchange.com/questions/261326/….
$endgroup$
– Anubhab Ghosal
Dec 8 '18 at 18:23
add a comment |
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$begingroup$
Have you tried making examples for small $n?$
$endgroup$
– saulspatz
Dec 8 '18 at 15:45
$begingroup$
Hint: You can find a recurrence for your answer by conditioning on whether or not $nin A$.
$endgroup$
– Mike Earnest
Dec 8 '18 at 17:47
1
$begingroup$
See math.stackexchange.com/questions/261326/….
$endgroup$
– Anubhab Ghosal
Dec 8 '18 at 18:23