Approximating $sumlimits_{rsubset S}|r|!prodlimits_{xin r}x$
There is a set $S={x_1, x_2, ..., x_N}.$
I'm trying to approximate this:
$$p(S)=sum_{rsubset S}|r|!prod_{xin r}x$$
I know that:
$$sum_{rsubset S}prod_{xin r}x=prod_{xin S}(1+x)$$
I was wondering if there is a way to approximate $p(S)$ with something.
An idea:
Change $x$ in $prodlimits_{xin S}(1+x)$ to $a(x)x$ so that:
$$prod_{xin S}(1+a(x)x)simsum_{rsubset S}|r|!prod_{xin r}x$$
I'm actually trying to do this:
$frac{sumlimits_{rsubset S}|r|!prodlimits_{xin r}x}{sumlimits_{rsubset S}(|r|-1)!prodlimits_{xin r}x}$
But I don't think there could be any shortcut.
combinatorics discrete-mathematics combinations approximation
asked 2 days ago
AnaisAnais
286
add a comment |
There is a set $S={x_1, x_2, ..., x_N}.$
I'm trying to approximate this:
$$p(S)=sum_{rsubset S}|r|!prod_{xin r}x$$
I know that:
$$sum_{rsubset S}prod_{xin r}x=prod_{xin S}(1+x)$$
I was wondering if there is a way to approximate $p(S)$ with something.
An idea:
Change $x$ in $prodlimits_{xin S}(1+x)$ to $a(x)x$ so that:
$$prod_{xin S}(1+a(x)x)simsum_{rsubset S}|r|!prod_{xin r}x$$
I'm actually trying to do this:
$frac{sumlimits_{rsubset S}|r|!prodlimits_{xin r}x}{sumlimits_{rsubset S}(|r|-1)!prodlimits_{xin r}x}$
But I don't think there could be any shortcut.
combinatorics discrete-mathematics combinations approximation
asked 2 days ago
AnaisAnais
286
add a comment |
There is a set $S={x_1, x_2, ..., x_N}.$
I'm trying to approximate this:
$$p(S)=sum_{rsubset S}|r|!prod_{xin r}x$$
I know that:
$$sum_{rsubset S}prod_{xin r}x=prod_{xin S}(1+x)$$
I was wondering if there is a way to approximate $p(S)$ with something.
An idea:
Change $x$ in $prodlimits_{xin S}(1+x)$ to $a(x)x$ so that:
$$prod_{xin S}(1+a(x)x)simsum_{rsubset S}|r|!prod_{xin r}x$$
I'm actually trying to do this:
$frac{sumlimits_{rsubset S}|r|!prodlimits_{xin r}x}{sumlimits_{rsubset S}(|r|-1)!prodlimits_{xin r}x}$
But I don't think there could be any shortcut.
combinatorics discrete-mathematics combinations approximation
asked 2 days ago
AnaisAnais
286
There is a set $S={x_1, x_2, ..., x_N}.$
I'm trying to approximate this:
$$p(S)=sum_{rsubset S}|r|!prod_{xin r}x$$
I know that:
$$sum_{rsubset S}prod_{xin r}x=prod_{xin S}(1+x)$$
I was wondering if there is a way to approximate $p(S)$ with something.
An idea:
Change $x$ in $prodlimits_{xin S}(1+x)$ to $a(x)x$ so that:
$$prod_{xin S}(1+a(x)x)simsum_{rsubset S}|r|!prod_{xin r}x$$
I'm actually trying to do this:
$frac{sumlimits_{rsubset S}|r|!prodlimits_{xin r}x}{sumlimits_{rsubset S}(|r|-1)!prodlimits_{xin r}x}$
But I don't think there could be any shortcut.
combinatorics discrete-mathematics combinations approximation
combinatorics discrete-mathematics combinations approximation
asked 2 days ago
AnaisAnais
286
asked 2 days ago
AnaisAnais
286
edited 18 hours ago
Anais
asked 2 days ago
AnaisAnais
286
asked 2 days ago
AnaisAnais
286
asked 2 days ago
AnaisAnais
286
286
add a comment |
add a comment |
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