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 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 Table of n, a(n) for n=1..11. 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 Cf. A185141, A002860. Sequence in context: A158269 A024257 A152653 * A172478 A087315 A081460 Adjacent sequences: A344690 A344691 A344692 * A344694 A344695 A344696 KEYWORD nonn AUTHOR Tanya Khovanova and MIT PRIMES STEP Senior group, Jun 11 2021 STATUS approved

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