Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A009997
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A009997 Number of comparative probability orderings on all subsets of n elements that can arise by assigning a probability distribution to the individual elements. +0
2
1, 1, 2, 14, 516, 124187, 214580603 (list; graph; listen)
OFFSET

1,3

COMMENT

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)

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.

LINKS

D. Maclagan, [math/9809134] Boolean Term Orders and the Root System B_n

CROSSREFS

Cf. A005806.

Sequence in context: A050561 A135865 A160710 this_sequence A048137 A005806 A015184

Adjacent sequences: A009994 A009995 A009996 this_sequence A009998 A009999 A010000

KEYWORD

nonn,hard,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

a(6) and a(7) from Diane Maclagan and Michael Kleber (maclagan(AT)math.berkeley.edu, michael.kleber(AT)gmail.com)

Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 26 2008

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified December 16 17:18 EST 2009. Contains 170825 sequences.


AT&T Labs Research