The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A344693 a(n) is the number of joint preference profiles in a stable marriage problem with n men and n women. 1
1, 4, 72, 13824, 19353600, 585252864000, 309856276316160000, 4385849628750224818176000, 2004821822925413274697731145728000, 36224269774123479086515914989912457216000000, 31014029806101314488308034499720939299674343342080000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A joint profile is defined as a preference profile with a fixed function f(k), such that for every man ranked k by a woman, he has to rank her back as f(k).
In such a profile the ranking matrix of women's preferences forms a Latin square. The same is true for men's preferences.
LINKS
FORMULA
a(n) = n!*A002860(n)
EXAMPLE
For n=2, there are two types of joint profiles. In the first type, the mutual rankings are (1,1) and (2,2). In the second type, the mutual rankings are (1,2) and (2,1). For each type, the profile is uniquely defined after choosing the woman to be the first choice for the first man (there are two ways to do it). Therefore, a(2) = 4.
CROSSREFS
Sequence in context: A158269 A024257 A152653 * A172478 A087315 A081460
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, Jun 11 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)