A342811 Volume of the permutohedron obtained from the coordinates 1, 2, 4, ..., 2^(n-1), multiplied by (n-1)!.

1, 13, 1009, 354161, 496376001, 2632501072321, 52080136110870785, 3872046158193220660993, 1099175272489026844687825921, 1210008580962784935280673680079873, 5225407816779297641534116390319222362113

Offset

2,2

Comments

Here the volume is relative to the unit cell of the lattice which is the intersection of Z^n with the hyperplane spanning the polytope.

a(n) is the number of subgraphs of the complete bipartite graph K_{n-1,n} such that for any vertex from the 2nd part there is a matching that covers all other vertices; Postnikov calls the characterization of such subgraphs "the dragon marriage problem".

Links

Table of n, a(n) for n=2..12.

Alexander Postnikov, Permutohedra, Associahedra, and Beyond, International Mathematics Research Notices, 2009, 1026-1106; arXiv:math/0507163 [math.CO], 2005. See Example 5.5.

Mathematica

a[n_] := Sum[(p.(2^Range[0, n-1]))^(n-1) / Times @@ Differences[p], {p, Permutations@Range@n}];
Table[a[n], {n, 2, 8}]

Crossrefs

Cf. A066319 (analog for regular permutohedron), A087422, A227414, A342812.

Sequence in context: A358983 A096084 A203708 * A301870 A297739 A128685

Adjacent sequences: A342808 A342809 A342810 * A342812 A342813 A342814

Keyword

nonn

Author

Andrey Zabolotskiy, Mar 22 2021

Status

approved