OFFSET
0,4
COMMENTS
The vertices are the n! permutation matrices. If A(p1) and A(p2) are two permutation matrices corresponding to permutations p1 and p2 the closed interval between these two matrices forms an edge of the polytope iff the permutation p1*(p2^-1) is a cycle, i.e. its cycle decomposition in the symmetric group S_n contains exactly one nontrivial cycle.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
FORMULA
a(n) = 1/2* n! * Sum_{k=2...n} C(n,k)*(k-1)!.
a(n) ~ Pi * n^(2*n) / exp(2*n - 1). - Vaclav Kotesovec, Jun 09 2019
EXAMPLE
a(3) = 15 because there are 3! = 6 vertices and C(6,2) intervals and in this case all are edges so a(3) = C(6,2) = 15.
MAPLE
with(combinat): for n from 1 to 30 do printf(`%d, `, 1/2* n! * sum(binomial(n, k)*(k-1)!, k=2..n)) od:
MATHEMATICA
a[n_] = If[n==0, 0, (n*n!/2)*(HypergeometricPFQ[{1, 1, 1-n}, {2}, -1]-1)]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 19 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Noam Katz (noamkj(AT)hotmail.com), Feb 20 2001
EXTENSIONS
More terms from James A. Sellers, Feb 21 2001
STATUS
approved