A344666 a(n) is the number of preference profiles in the stable marriage problem with 3 men and 3 women that generate n possible stable matchings.

34080, 11484, 1092

Offset

1,1

Comments

A185141(n) is the total number of preference profiles for n men and n women.

A185141(3) = 46656 is the sum of the terms of this sequence.

For 2 men and 2 women, the total number of preference profiles is 16, where 14 profiles have 1 stable matching, and 2 profiles have 2 stable matchings.

For 4 men and 4 women, the total number of preference profiles is 110075314176, where the number of possible stable matchings ranges from 1 to 10, excluding 9. The distribution is provided by sequence A344667(n).

Links

Table of n, a(n) for n=1..3.

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.

Crossrefs

Cf. A185141, A344667, A344668, A344669.

Sequence in context: A231196 A212229 A204669 * A227699 A234820 A182292

Adjacent sequences: A344663 A344664 A344665 * A344667 A344668 A344669

Keyword

nonn,bref,fini,full

Author

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

Status

approved