An uncertainty principle for Möbius inversion on posets
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912932712939520 |
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| author | Goh, Marcel K. |
| author_facet | Goh, Marcel K. |
| contents | We give conditions for a locally finite poset $P$ to have the property that for any functions $f:P\to {\bf C}$ and $g:P\to {\bf C}$ 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 non-examples are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02466 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An uncertainty principle for Möbius inversion on posets Goh, Marcel K. Combinatorics 06A07 We give conditions for a locally finite poset $P$ to have the property that for any functions $f:P\to {\bf C}$ and $g:P\to {\bf C}$ 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 non-examples are discussed. |
| title | An uncertainty principle for Möbius inversion on posets |
| topic | Combinatorics 06A07 |
| url | https://arxiv.org/abs/2302.02466 |