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math.RT2025
Sharp character bounds and cutoff for symmetric groups
Sam Olesker-Taylor, Lucas Teyssier, Paul Thévenin
We develop a flexible technique to bound the characters of symmetric groups, via the Naruse hook length formula, the Larsen--Shalev character bounds, and appropriate diagram slicin…
math.RT2025
Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function
Lucas Teyssier, Paul Thévenin
We prove sharp bounds on the virtual degrees introduced by Larsen and Shalev. This leads to improved bounds on characters of symmetric groups. We then sharpen bounds of Liebeck and…