I'm a big fan of the Online Encylopedia of Integer Sequences,
both as a hobby and as a research tool.
My user profile.
Sequences Authored
A309933. Table read by rows: T(n,k)
is the number of stable marriage instances with n men and n+1 women in which
some "rejecting" woman receives exactly k proposals.
Analyzing this one has interesting applications to the theory of random
stable matching markets, as described in our
paper.
Contributions
A005154. Number of stable matchings.
This sequence is the best known lower bound on the maximum number of
stable matchings on n men and n women.
An analysis of the growth of this sequence was known, but never published.
With some help from Peter Shor this analysis is finally
available
here.
A116078. Number of antichains in a
cylinder poset.
One way to prove upper bounds on the worst-case maximum number of stable
marriages is to prove upper bounds on the number of antichains in
"tangled \(n \times n\) grid" posets, as observed by
Dömötör
Pálvölgyi.
There is a simple tangled grid poset whose number of antichains is exactly
A116078, as we show
here.
This sequence grows like \( \sqrt{n} 4^n \).
This by itself disproves Pálvölgyi's conjecture that tangled \(n \times n\) grids have
at most \(4^n\) antichains, and a modification of the analysis I gave
for A005154
here
actually proves that tangled grids can have
up to \( 4.17^n \) antichains.
A144685 and A144686.
Two sequences regarding Condorcet Domains from social choice theory.
A lot of interesting combinatorial questions arise from investigating sets
of linear orders over which majority voting never produces cycles.