In python, given a list mylist of lists el of integers, I would like to remove duplicates that are equivalent under specific permutations of the indices. The question is more general but I have in mind "decorated" McKay graphs where each node is given an integer defining el whose sum is equal to a certain number. Generating mylist is easy enough, but there is a lot of redundancy depending on the symmetry of the graph. For instance, for the "D4" diagram, el represents the following decorated graph: a | el = [a, b, c, d, e] <--> b-c―d | e The two lists [1,0,4,0,0] and [0,0,4,0,1] are duplicates because there are the same up to a reflection of the graph around the horizontal axis. More generally, the lists el duplicates if there are equivalent under any permutation of a,b,d,e. Is there a simple way of removing duplicates given an arbitrary symmetry? The way I did it for this particular graph was to sort the indices 0,1,3,4 and compare: from itertools import product def check_duplicate(f, li): for l in li: if l[2] == f[2] and sorted(l[:2] + l[3:]) == sorted(f[:2] + f[3:]): return True return False mylist = [list(i) for i in product(range(5), repeat=5) if sum(i) == 5] newlist = [] for f in my_list: if check_duplicate(f, newlist) == False: newlist.append(f) Here tmp is generated brute force, but the condition is more involved in my real case. This works well enough for this particular example, but is a bit clunky, and the implementation is harder to generalize to more involved cases. Is there a way to remove the duplicates in a more optimized way, in particular one that can easily implement removing duplicates given a particular symmetry of the indices of el? Continue reading...
