The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A344665 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A344665

a(n) is the number of preference profiles in the stable marriage problem with n men and n women, where both the men's preferences and women's preferences form a Latin square when arranged in a matrix, with no paired man and woman who rank each other first.
(history; published version)

#21 by Michael De Vlieger at Sat Jun 01 19:28:57 EDT 2024

STATUS

reviewed

approved

#20 by Jon E. Schoenfield at Sat Jun 01 12:18:54 EDT 2024

STATUS

proposed

reviewed

#19 by Joerg Arndt at Sat Jun 01 02:52:36 EDT 2024

STATUS

editing

proposed

Discussion

Sat Jun 01

12:18

Jon E. Schoenfield: ’Looks good to me!

#18 by Joerg Arndt at Sat Jun 01 02:52:11 EDT 2024

FORMULA

a(n) = (A002860(n)^2/n!) * Sum_{i=0..n} (-1)^i * n!/i! = A344664(n) * A000166(n).

STATUS

proposed

editing

Discussion

Sat Jun 01

02:52

Joerg Arndt: like this then?

#17 by Joerg Arndt at Sat Jun 01 02:51:28 EDT 2024

STATUS

editing

proposed

#16 by Joerg Arndt at Sat Jun 01 02:51:22 EDT 2024

FORMULA

a(n) = (A002860(n)^2/n!) * Sum_{i=0..n} [(-1)^i * n!/i!] = A344664(n) * A000166(n).

STATUS

proposed

editing

#15 by Jon E. Schoenfield at Fri May 31 23:31:36 EDT 2024

STATUS

editing

proposed

Discussion

Sat Jun 01

01:16

Michel Marcus: no they are not necessary

01:17

Michel Marcus: Sum_{i=0..n} (-1)^i * n!/i!   is A000166(n)   (same formula, but n! out of the sum, there)

#14 by Jon E. Schoenfield at Fri May 31 23:29:55 EDT 2024

NAME

a(n) is the number of preference profiles in the stable marriage problem with n men and n women, where both the men's preferences and women's preferences form a Latin square when arranged in a matrix, with no paired man and woman paired who rank each other first.

FORMULA

a(n) = (A002860(n)^2/n! ) * Sum_{i=0...n} [(-1)^i * n!/i!] = A344664(n) * A000166(n).

STATUS

proposed

editing

Discussion

Fri May 31

23:30

Jon E. Schoenfield: Thanks!

23:31

Jon E. Schoenfield: Are the square brackets in the Formula entry necessary?

#13 by Jon E. Schoenfield at Fri May 31 21:24:14 EDT 2024

STATUS

editing

proposed

Discussion

Fri May 31

22:06

Michael De Vlieger: "no paired man and woman" better?

#12 by Jon E. Schoenfield at Fri May 31 21:23:58 EDT 2024

NAME

a(n) is the number of preference profiles in the stable marriage problem with n men and n women, where both the men’'s preferences and women’'s preferences form a Latin square when arranged in a matrix, with no man and woman pairs paired who rank each other first.

EXAMPLE

For n = 2, there are A002860(2) = 2 ways to set up the men’'s profiles. Since the women don’'t want to rank the man who ranked them first as first, there is exactly 1 way to set up the women’'s profiles. So, there are 2 * 1 = 2 preference profiles for n = 2.

STATUS

approved

editing

Discussion

Fri May 31

21:24

Jon E. Schoenfield: "pairs" -> "paired" okay?