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COMMENTS
| Also 1/(2^n*n!) * number of regions of hyperplane arrangements with normals (0,1,-1)^n
Comment from David Wilson, Aug 15, 2008: (Start) Also, number of possible orderings of the set of divisors of a product of n distinct primes.
Let p1 < p2 < ... < p_n be primes (say p1 = p, p2 = q, p3 = r, ...) Consider the set M of divisors of p1*p2*...*p_n. How many ways can M be ordered?
For n = 0, we have m = { 1 }, with 1 ordering.
For n = 1, we have M = { 1, p }. There is 1 possible ordering, 1 < p.
For n = 2, we have M = { 1, p, q, pq }. Remembering p < q, there is again 1 possible ordering, 1 < p < q < pq.
For n = 3, we have M = { 1, p, q, r, pq, pr, qr, pqr }. There are 2 possible orderings here:
1 < p < q < r < pq < pr < qr < pqr,
1 < p < q < pq < r < pr < qr < pqr. (End)
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REFERENCES
| T. Fine and J. Gill, Comparative probability relations, Ann. Prob. 4 (1976) 667-673.
D. Maclagan, Boolean Term Orders and the Root System B_n, Order 15 (1999), 279-295.
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