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A337083

Number of spanning trees of the 1-skeleton of the (n-1)-dimensional permutohedron.

1, 1, 6, 101154816, 6187732257761496793412385090375984958331031826464768000000000

OFFSET

1,3

COMMENTS

We have the factorizations:

a(4) = 2^15 * 3^2 * 7^3.

a(5) = 2^59 * 3^15 * 5^9 * 7^5 * 11^6 * 23^5 * 29^4 * 41^4.

a(6) = 2^215 * 3^178 * 5^47 * 7^15 * 11^39 * 13^10 * 19^16 * 23^15 * 29^16 * 41^16 * 61^5 * 67^9 * 71^5 * 1931^16 * 3253^9.

LINKS

Eric Weisstein's World of Mathematics, Bruhat Graph.

EXAMPLE

For n=3 the permutohedron is a hexagon, which has six spanning trees.

PROG

(Python)

import sympy, itertools

def A337083(n):

p=tuple(itertools.permutations(range(n)))

m=len(p)

q={p[i]:i for i in range(m)}

Q=sympy.diag(*[n-1]*m)

for i in range(m):

for k in range(n-1):

Q[i, q[p[i][:k]+tuple(reversed(p[i][k:k+2]))+p[i][k+2:]]]=-1

return Q[:m-1, :m-1].det() # Pontus von Brömssen, Jan 18 2021

CROSSREFS

KEYWORD

nonn

AUTHOR

EXTENSIONS

a(1) prepended by Pontus von Brömssen, Jan 19 2021

STATUS

approved

URL: https://oeis.org/A337083