In need of interpretation of a ordered-subset related problem.
$begingroup$
''Given a set $S_n = {1, 2, 3, ldots, n}$, we define a preference list to be an ordered subset of $S_n$. Let $P_n$ be the number of preference lists of $S_n$. Show that for positive integers $n > m$, $P_n - P_m$ is divisible by $n - m$.
Note: the empty set and $S_n$ are subsets of $S_n$.''
Can anyone help me out to make me understand the problem ? (giving an explained example of this question will be very good )
Thanks in advance :)
combinatorics number-theory
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
$endgroup$
add a comment |
$begingroup$
''Given a set $S_n = {1, 2, 3, ldots, n}$, we define a preference list to be an ordered subset of $S_n$. Let $P_n$ be the number of preference lists of $S_n$. Show that for positive integers $n > m$, $P_n - P_m$ is divisible by $n - m$.
Note: the empty set and $S_n$ are subsets of $S_n$.''
Can anyone help me out to make me understand the problem ? (giving an explained example of this question will be very good )
Thanks in advance :)
combinatorics number-theory
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
$endgroup$
add a comment |
$begingroup$
''Given a set $S_n = {1, 2, 3, ldots, n}$, we define a preference list to be an ordered subset of $S_n$. Let $P_n$ be the number of preference lists of $S_n$. Show that for positive integers $n > m$, $P_n - P_m$ is divisible by $n - m$.
Note: the empty set and $S_n$ are subsets of $S_n$.''
Can anyone help me out to make me understand the problem ? (giving an explained example of this question will be very good )
Thanks in advance :)
combinatorics number-theory
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
$endgroup$
''Given a set $S_n = {1, 2, 3, ldots, n}$, we define a preference list to be an ordered subset of $S_n$. Let $P_n$ be the number of preference lists of $S_n$. Show that for positive integers $n > m$, $P_n - P_m$ is divisible by $n - m$.
Note: the empty set and $S_n$ are subsets of $S_n$.''
Can anyone help me out to make me understand the problem ? (giving an explained example of this question will be very good )
Thanks in advance :)
combinatorics number-theory
combinatorics number-theory
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
asked Dec 29 '18 at 13:10
nahin munkarnahin munkar
1
1
add a comment |
add a comment |
1 Answer
1
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$begingroup$
For example, for $n=3$ the preference lists of ${1,2,3}$ are
$$ emptyset\
(1)\
(2)\
(3)\
(1, 2)\
(2, 1)\
(1, 3)\
(3, 1)\
(2, 3)\
(3, 2)\
(1, 2, 3)\
(1, 3, 2)\
(2, 1, 3)\
(2, 3, 1)\
(3, 1, 2)\
(3, 2, 1)$$
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
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1 Answer
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1 Answer
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active
oldest
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active
oldest
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active
oldest
votes
$begingroup$
For example, for $n=3$ the preference lists of ${1,2,3}$ are
$$ emptyset\
(1)\
(2)\
(3)\
(1, 2)\
(2, 1)\
(1, 3)\
(3, 1)\
(2, 3)\
(3, 2)\
(1, 2, 3)\
(1, 3, 2)\
(2, 1, 3)\
(2, 3, 1)\
(3, 1, 2)\
(3, 2, 1)$$
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
$endgroup$
add a comment |
$begingroup$
For example, for $n=3$ the preference lists of ${1,2,3}$ are
$$ emptyset\
(1)\
(2)\
(3)\
(1, 2)\
(2, 1)\
(1, 3)\
(3, 1)\
(2, 3)\
(3, 2)\
(1, 2, 3)\
(1, 3, 2)\
(2, 1, 3)\
(2, 3, 1)\
(3, 1, 2)\
(3, 2, 1)$$
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
$endgroup$
add a comment |
$begingroup$
For example, for $n=3$ the preference lists of ${1,2,3}$ are
$$ emptyset\
(1)\
(2)\
(3)\
(1, 2)\
(2, 1)\
(1, 3)\
(3, 1)\
(2, 3)\
(3, 2)\
(1, 2, 3)\
(1, 3, 2)\
(2, 1, 3)\
(2, 3, 1)\
(3, 1, 2)\
(3, 2, 1)$$
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
$endgroup$
For example, for $n=3$ the preference lists of ${1,2,3}$ are
$$ emptyset\
(1)\
(2)\
(3)\
(1, 2)\
(2, 1)\
(1, 3)\
(3, 1)\
(2, 3)\
(3, 2)\
(1, 2, 3)\
(1, 3, 2)\
(2, 1, 3)\
(2, 3, 1)\
(3, 1, 2)\
(3, 2, 1)$$
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
answered Dec 29 '18 at 14:13
awkwardawkward
6,92511026
6,92511026
add a comment |
add a comment |
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