An uncertainty principle for Möbius inversion on posets
DOI:
https://doi.org/10.55016/6ej3y980Abstract
We give conditions for a locally finite join-semilattice $P$ to have the property that for any functions $f:P\to \mathbb{C}$ and $g:P\to \mathbb{C}$ not identically zero and linked by the Möbius inversion formula, the support of at least one of $f$ and $g$ is infinite. This generalises and gives an entirely poset-theoretic proof of a result of Pollack. Various examples and nonexamples are discussed.
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