[seqfan] Re: Two Sequences Related To Permutations of (1,2,...,n)
eclark at math.usf.edu
Sun Jan 18 01:39:17 CET 2009
On Sat, 17 Jan 2009, Leroy Quet wrote:
> Let a(n) = the number of permutations (p(1),p(2),p(3)...,p(n)) of (1,2,3,...,n) where, if each (m,p(m)) is plotted on a graph, then the entire set P of the n of these plotted points would be on the perimeter of the convex hull of P.
> For instance, for n = 5:
> (p(1),p(2),p(3),p(4),p(5)) = (1,3,5,2,4) would be included in the count, but
> (1,4,3,2,5) would not because point (3,3) is not on the perimeter of the convex hull of P.
Isn't this the same as
...number of weakly unimodal permutations of 1..n, that is, permutations
with exactly one local maximum.
If so the formula is 2^(n-1).
More information about the SeqFan