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A344669 a(n) is the number of preference profiles in the stable marriage problem with n men and n women that generate the maximum possible number of stable matchings. 6
1, 2, 1092, 144, 507254400 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
From Dan Eilers, Dec 23 2023: (Start)
A357271 provides the best known lower bounds for the maximum number of stable matchings of order n.
A357269 provides exact results. (End)
LINKS
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.
FORMULA
a(n) = A368433(n) * A010790(n-1). - Dan Eilers, Dec 24 2023
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) = 2.
CROSSREFS
Sequence in context: A108963 A152510 A324590 * A321633 A244550 A359952
KEYWORD
nonn,bref,more
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, May 27 2021
EXTENSIONS
a(5) from Dan Eilers, Dec 23 2023
STATUS
approved

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