Assume, there is a set of symbolic positive numbers in an ascending order (e.g., $a\leq b \leq c \leq d$). Is there a combinatorial algorithm that outputs all possible order relationships between $a, b, c, d$ and the sums of all possible subsets of this set, e.g.:
$a\leq b \leq a+b \leq c \leq a+c\leq \ldots \leq a+b+c+d$
Any hints or references are much appreciated. Many thanks and regards!
