Is there a theory or branch of Math which considers systems of equations in which the subscript variables can be permuted to obtain the same system, ie, they are invariant under some permutations.
Example the system: x3(x2+x4)=x2(x1+x4)=x1(x3+x4) is invariant under the group of perms {identity, (123),(132)}.
Does knowing the group help you solve the system?
Are there any papers on this topic?
Note the group isn't the whole symmetric group on {1,2,3}, perm (12) doesn't work.
I'm interested when the xi are positive integers, but also arbitrary variables.
Thanks for any info.