A005806 Number of comparative probability orderings on n elements. (Formerly M2072)

1, 1, 1, 2, 14, 546, 169444, 560043206

Offset

0,4

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..7.

Andrew Beveridge, Ian Calaway, and Kristin Heysse, de Finetti Lattices and Magog Triangles, arXiv:1912.12319 [math.CO], 2019.

T. Fine and J. Gill, The enumeration of comparative probability relations, Ann. Prob. 4 (1976) 667-673.

D. Maclagan, Boolean Term Orders and the Root System B_n, arXiv:math/9809134 [math.CO], 1998-1999.

D. Maclagan, Boolean Term Orders and the Root System B_n, Order 15 (1999), 279-295.

Formula

a(n) >= A009997(n) with equality iff n < 5. - M. F. Hasler, Mar 17 2023

Example

For n = 3, the two orders are 1 < 2 < 12 < 3 < 13 < 23 < 123 and 1 < 2 < 3 < 12 < 13 < 23 < 123.
For zero elements, there is exactly one ordering. - M. F. Hasler, Mar 17 2023

Crossrefs

Cf. A009997.

Sequence in context: A009997 A328377 A048137 * A015184 A012002 A012005

Adjacent sequences: A005803 A005804 A005805 * A005807 A005808 A005809

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane

Extensions

a(7) from Diane Maclagan and Michael Kleber

Status

approved