A378609 Number of weak orderings of (i,j), 1 <= i,j <= n, for which there is a set X = {x_1<...

1, 1, 3, 25, 477, 18403

Offset: 1

Author

Kevin O'Bryant, Dec 01 2024

Keywords

• nonn
• hard
• more

Comments

Number of weak orderings of (i,j), 1<=i,j<=n, for which there is a set X={x_1<...

Number of weak orderings of (i,j), 1<=i,j<=n, for which there is a set X={x_1<...

Examples

			For n=3 the three weak orderings are: 11<12=21<13=31=22<23=32<33, 11<12=21<22<13=31<23=32<33, and 11<12=21<13=31<22<23=32<33, which arise from the sets {1,2,3}, {1,2,4}, and {1,3,4}, respectively.
For n=4, there are 39 weak orderings, but only 25 arise from sets of real numbers. For example, the weak ordering 11<12=21<13=31<22<14=41=23=32<24=42=33<34=43<44 does not arise from any set of real numbers.
		

Links

• Kevin O'Bryant, Visualizing the sum-product conjecture, arXiv:2411.08139 [math.NT], 2024.

Crossrefs

Cf. A376162.

Formula

a(n) <= A376162(n).

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