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- W4367000495 abstract "We study the zero-sharing behavior among irreducible characters of a finite group. For symmetric groups $S_n$, it is proved that, with one exception, any two irreducible characters have at least one common zero. To further explore this phenomenon, we introduce the common-zero graph of a finite group $G$, with non-linear irreducible characters of $G$ as vertices, and edges connecting characters that vanish on some common group element. We show that for solvable and simple groups, the number of connected components of this graph is bounded above by 3. Lastly, the result for $S_n$ is applied to prove the non-equivalence of the metrics on permutations induced from faithful irreducible characters of the group." @default.
- W4367000495 created "2023-04-27" @default.
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- W4367000495 date "2023-04-24" @default.
- W4367000495 modified "2023-09-24" @default.
- W4367000495 title "Common zeros of irreducible characters" @default.
- W4367000495 doi "https://doi.org/10.48550/arxiv.2304.12253" @default.
- W4367000495 hasPublicationYear "2023" @default.
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