2 problems
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Gershnik et al.'s conjecture on totally extremal ideal Perron similarities
Gershnik et al.'s conjecture. Every totally extremal normalized ideal Perron similarity is the character table of a finite Abelian group.
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Character-table characterization of totally extremal ideal Perron similarities
Character-table conjecture. If is a normalized ideal Perron similarity and is totally extremal, then is the character table of a finite Abelian group.