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A293153
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Number of linear extensions of a certain poset C^bar_n.
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1
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1, 2, 12, 150, 3192, 103050, 4686660, 285159966, 22346336880, 2190484006290, 262452778322940, 37721725955429670, 6403456745121882600, 1267187306764190765850, 289083710604023135810100, 75296935345163706056184750, 22204989048146847440246995680, 7359190013115437279346917463330
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OFFSET
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0,2
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COMMENTS
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Exercise 12 of Morales et al. says that a(n) is the number of permutations (a_1,...,a_n,b_1,...b_n) in S_{2n} such that a_i < b_j for all 1 <= i < j <= n.
This is also the number of permutations in the interval [id, (2*n,n,2*n-1,n-1,...,n+1,1)] in the weak Bruhat order of permutations. - Alejandro H. Morales, Aug 20 2024
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LINKS
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PROG
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(Rust)
use permutator::heap_permutation;
fn main() {
for n in 1..=7 {
let mut c = 0;
heap_permutation(&mut Vec::from_iter(0..2*n), |p| c += ok(p, n) as u64);
println!("{c}");
}
}
fn ok(p: &[usize], n: usize) -> bool {
for i in 0..n {
for j in i+1..n {
if p[i] > p[n+j] {
return false
}
}
}
true
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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