To clarify: by unique I mean disregarding permutation of variables. Say I have n variables, and want to generate all "unique" polynomials of degree 2 and 1 (powers are excluded). For example, for n = 3, x1 x2 and x3 are the variables.
x1x2 or x1x2 + x2x3 or x1x3 + x1 or x3 are all example polynomials.
But, x1x2 + x3 can be considered the same polynomial as x1x3 + x2, since variables are simply swapped. I'd like to generate only the "unique" polynomials, (in this case, x1x2 + x3, x1x3 + x2, x2x3 + x1 would all be considered the same under permutation of variables).
I think the polya enumeration theorem is applicable here, but i'm not quite sure how to use it.
Thanks for the help!