Deck the Halls
by cjquines0, Dec 26, 2016, 10:58 AM
Canada 2006/3 wrote:
In a rectangular array of nonnegative reals with 
rows and 
columns, each row and each column contains at least one positive element. Moreover, if a row and a column intersect in a positive element, then the sums of their elements are the same. Prove that 
.
rows and 
columns, each row and each column contains at least one positive element. Moreover, if a row and a column intersect in a positive element, then the sums of their elements are the same. Prove that 
.
with bipartite sets 
and 
,
and 
if the intersection of 
and 
is positive.
such that 
.
be 
and the sums of the columns in 
be 
.
.
as all the other elements in the rows of 
because the other entries in the columns are nonnegative anyway. Combining these yields 
But note that each of the 
s
s
,
for all subsets 
.
,
,
May 2017
April 2017