On the number of non-zero character values in generalized blocks of symmetric groups

TL;DR

This paper investigates the count of irreducible characters in generalized blocks of symmetric groups that are non-zero on specific conjugacy classes, providing lower bounds for these counts.

Contribution

It introduces new lower bounds for the number of non-vanishing irreducible characters in generalized blocks of symmetric groups on given conjugacy classes.

Findings

Established lower bounds for non-zero character counts

Analyzed the structure of generalized e-blocks in symmetric groups

Provided insights into character vanishing behavior

Abstract

Given a generalized $e$-block $B$ of a symmetric group and an $e$-regular conjugacy class $C$, we study the number of irreducible characters in $B$ which do not vanish on $C$ and find lower bounds for it.