function part = next_partition(part)
% A partition of n is represented as a row vector, in descending order.  
% This function returns the next partition of n.

if part(1) == 1
    part = [];
    return
end

n = sum(part);

l = length(part);
i = l;
while part(i) == 1
    i = i - 1;
end

part(i) = part(i) - 1;

if part(i) == 1
    part(l + 1) = 1;
    return
end

left = n - sum(part(1:i));

while left > 0
    i = i + 1;
    part(i) = min(left, part(i - 1));
    left = left - part(i);
end
part = part(1:i);