Need help understanding place invariants as used in place-transition nets

Suppose I know the markings of a given place-transition net.

How do I determine which of the markings is a place invariant? I also know the initial marking. I will appreciate a very easy-to-digest explanation.

I have read page 17 of this paper, where the formula for finding place invariants is described but I do not understand it fully.

Please do not simply tell me what the place invariants are. Explain to me how I can find them so that I can always do this in the future.

Initial marking for a set of places (U,V,W,X,Y,Z):

• (0,1,1,1,0,0)

Other markings:

1. (0,1,0,0,1,0)
2. (0,1,0,1,0,1)
3. (1,0,0,1,0,0)

I later learned that if the set of places is (U,V,W,X,Y,Z), then the place invariants are the sets for which the sum of tokens remains the same for every marking.

So, the sets of places that form place invariants are:

1. (U,V) - sum of tokens is 1 for every marking.
2. (U, W, Y, Z) - sum is 1.
3. (U, V, X, Y) - sum is 2.
4. (X, Y) - sum is 1.