A014627 - OEIS

A014627

Consider all complete bipartite graphs on 2n nodes and all possible assignment of weights w(i) (for nodes i=1,...,2n); sequence gives maximal number of ways to orient the edges of the graph so that each node i has w(i) edges oriented towards it (for i=1,...,2n).

%I #3 Feb 27 2009 03:00:00

%S 1,1,2,3,6,15,90,310,1860,8280,163560,1346940,21476700

%N Consider all complete bipartite graphs on 2n nodes and all possible assignment of weights w(i) (for nodes i=1,...,2n); sequence gives maximal number of ways to orient the edges of the graph so that each node i has w(i) edges oriented towards it (for i=1,...,2n).

%D D. Z. Djokovic and J. Sanmiya, Three Identities for Symmetric Polynomials over Z/2Z, preprint, 1999.

%e For n=2 the maximal bipartite graph has two nodes on each side and the weight of every node 1. The edges form a path which can be oriented forwards or backwards to give exactly one edge oriented towards each node. Thus for n=2 the sequence value is 2.

%K nonn

%O 1,3

%A Jason Scott Sanmiya (jssanmiy(AT)undergrad.math.uwaterloo.ca)