Question: Linking Parent Inventory To Variations

Is it possible to link a parent product inventory with it's linked variation group when configured as one product?

Functionality: Any cart purchase would decrease the parent and child variations at the same time automatically.

I know this can be done with options, but can't figure this out for variations configured as as one product.

Example Product:

Sticker decals that are printed on-demand. The decal paper is the only inventory to be tracked. Customers can choose different designs, but inventory and discounts are linked to the parent product / variation group.

Catalog Item: Sticker

Feature: Sticker Images
Variations: New products / codes for each different sticker image

In this case use product options, not variations