Vanishing pairs of conjugacy classes for the symmetric group | Synapse
October 16, 2025Open Access
Vanishing pairs of conjugacy classes for the symmetric group
Key Points
Pairs of conjugacy classes are identified where non-linear irreducible characters vanish on one class.
The classification reveals specific relationships between the conjugacy classes and their irreducible characters.
Understanding these pairs enhances mathematical insights into the structure of the symmetric group.
This analysis could improve the approach to studying other aspects of group theory.
Abstract
In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.