OFFSET
1,2
COMMENTS
Equivalently, these are the profiles where each woman is ranked differently by the n men.
Equivalently, for every rank i, there is exactly one woman who is ranked i by a given man.
The men-proposing Gale-Shapley algorithm on such a set of preferences ends in one round, since every woman receives one proposal in the first round.
Due to symmetry, a(n) is the number of preference profiles in the stable marriage problem with n men and n women, such that the women’s preference profiles form a Latin square.
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.
Wikipedia, Gale-Shapley algorithm.
FORMULA
a(n) = n!^n * A002860(n).
EXAMPLE
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, May 25 2021
STATUS
approved