Given a list of sets like: sets=[{1,2},{2,3},{1,3}] the product (1,2,3) will be generated twice in itertools.product(*sets), as the literals (1,2,3) and (2,3,1), because there is a loop. If there is no loop there will be no duplication, even though there might be lots of commonality between sets. A loop is formed to A in a set when you travel to B in the same set and then to B in another set that has A or to B in another set with C which connects to a set with A. e.g. 1>2--2>3--3>1 where '--' indicates movement between sets and '>' indicates movement within the set. The smallest loop would involve a pair of numbers in common between two sets, e.g. a>b--b>a. {edit: @ravenspoint's notation is nice, I suggest using {a}-b-{a} instead of the above.} Loops in canonical form should not have a bridging value used: either this represents a case where the loop traced back on itself (like in a cursive "i") or there is a smaller loops that could be made (like the outer and inner squares on the Arch de Triumph](https://commons.wikimedia.org/wiki/File:Paris_Arc_de_Triomphe.jpg). What type of graph structure could I be using to represent this? I have tried representing each set as a node and then indicating which sets are connected to which, but this is not right since for [{1,2},{1,3},{1,4}], there is a connection between all sets -- the common 1-- but there is no loop. I have also tried assigning a letter to each number in each set, but that doesn't seem right, either, since then I don't know how to discriminate against loops within a set. This was motivated by this question about generating unique products. Sample sets like the following (which has the trivial loop 4>17--17>4 and longer loops like 13>5--5>11--11>13) [{1, 13, 5}, {11, 13}, {17, 11, 4, 5}, {17, 4, 1}] can be generated as shown in the docstring of core. Alternate visualization analogy Another way to visualize the "path/loop" is to think of coloring points on a grid: columns contain elements of the sets and equal elements are in the same row. A loop is a path that starts at one point and ends at the same point by travelling vertically or horizontally from point to point and must include both directions of motion. A suitable permutation of rows and columns would reveal a staircase polygon. Continue reading...
