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I discovered an intriguing linear algebra relationship which I call a multijection. I'd like to share a version of this result, which will be understandable to a general math audience.

I used the multijection to solve an open problem about higher-dimensional sandpile groups, but I think that it has more to say. Some potentially relevant buzzwords are "positroids", "toric varieties", "Pontryagin duality", "Ehrhart theory", and "periodic tilings".