A344668 - OEIS

A344668

a(n) is the number of preference profiles in the stable marriage problem with n men and n women that generate exactly 1 possible stable matching.

1, 14, 34080, 65867261184

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OFFSET

1,2

COMMENTS

A069124(n) provides the lower bound for the maximum number of stable matchings with n men and n women. It is exact for n below 5.

LINKS

Table of n, a(n) for n=1..4.

Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, Sequences of the Stable Matching Problem, arXiv:2201.00645 [math.HO], 2021.

EXAMPLE

For n=2, there are 16 possible preference profiles: 14 of them generate one stable matching and 2 of them generate two stable matchings. Thus, a(2) = 14.

CROSSREFS

Cf. A069124, A185141, A344666, A344667, A344669.

Sequence in context: A053870 A283840 A079176 * A013754 A073940 A164322

Adjacent sequences: A344665 A344666 A344667 * A344669 A344670 A344671

KEYWORD

nonn,more

AUTHOR

Tanya Khovanova and MIT PRIMES STEP Senior group, May 27 2021

STATUS

approved