Common and Sidorenko equations in Abelian groups
| Autor: | Versteegen, Leo |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | A linear configuration is said to be common in a finite Abelian group $G$ if for every 2-coloring of $G$ the number of monochromatic instances of the configuration is at least as large as for a randomly chosen coloring. Saad and Wolf conjectured that if a configuration is defined as the solution set of a single homogeneous equation over $G$, then it is common in $\mathbb{F}_p^n$ if and only if the equation's coefficients can be partitioned into pairs that sum to zero mod $p$. This was proven by Fox, Pham and Zhao for sufficiently large $n$. We generalize their result to all sufficiently large Abelian groups $G$ for which the equation's coefficients are coprime to $\vert G\vert$ Comment: The content of this article was previously posted as part of arXiv:2106.06846 |
| Databáze: | arXiv |
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