A005806 Number of comparative probability orderings on n elements.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard
• more

Examples

			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
		

References

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

Links

• 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.

Crossrefs

Cf. A009997.

Formula

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

Extensions

a(7) from Diane Maclagan and Michael Kleber