|
|
A037302
|
|
Normalized volume of Birkhoff polytope of n X n doubly-stochastic square matrices. If the volume is v(n), then a(n) = ((n-1)^2)! * v(n) / n^(n-1).
|
|
3
|
|
|
1, 1, 3, 352, 4718075, 14666561365176, 17832560768358341943028, 12816077964079346687829905128694016, 7658969897501574748537755050756794492337074203099, 5091038988117504946842559205930853037841762820367901333706255223000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
The Birkhoff polytope is an (n-1)^2-dimensional polytope in n^2-dimensional space; its vertices are the n! permutation matrices.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(2)=1: The polytope of 2 X 2 matrices is the line segment from (1,0;0,1) to (0,1;1,0), with length v(2)=2, so a(2) = 1! * 2 / 2^1 = 1.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,hard,nice
|
|
AUTHOR
|
Günter M. Ziegler (ziegler(AT)math.tu-berlin.de)
|
|
EXTENSIONS
|
v(9) computed by Matthias Beck (matthias(AT)math.binghamton.edu) and Dennis Pixton (dennis(AT)math.binghamton.edu), Feb 25 2002
a(10) is based on a calculation of v(10) by Matthias Beck (matthias(AT)math.binghamton.edu) and Dennis Pixton (dennis(AT)math.binghamton.edu) from Mar 13 2002 to May 18 2003
|
|
STATUS
|
approved
|
|
|
|