Is there a notation that expresses a summation over all order-independent combinations of two variables? I have a single set of objects and want to show the summation of the joint probabilities of each unordered pair of those objects. I want it to be clear I'm not counting duplicate pairs, because the order of the elements doesn't matter.
For example, if I have the set:
w = [dog, cat, bear]
I want to convey:
Z = P(dog, cat) + P(dog, bear) + P(cat, bear)
Z = P(dog, cat) + P(dog, bear) + P(cat, dog) + P(cat, bear) + P(bear, dog) + P(bear, cat)