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.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 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

%I #7 Jan 27 2022 23:16:33

%S 1,4,72,13824,19353600,585252864000,309856276316160000,

%T 4385849628750224818176000,2004821822925413274697731145728000,

%U 36224269774123479086515914989912457216000000,31014029806101314488308034499720939299674343342080000000

%N a(n) is the number of joint preference profiles in a stable marriage problem with n men and n women.

%C 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).

%C In such a profile the ranking matrix of women's preferences forms a Latin square. The same is true for men's preferences.

%F a(n) = n!*A002860(n)

%e 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.

%Y Cf. A185141, A002860.

%K nonn

%O 1,2

%A _Tanya Khovanova_ and MIT PRIMES STEP Senior group, Jun 11 2021

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.

Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)