Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 160 / 2 / b / i

Table of contents
- Solution i

Solution

The Murnaghan–Nakayama rule states that if a permutation has a

k

-cycle and remaining cycle type

ρ

, then

χ^{λ} (k, ρ) = \sum_{H} (- 1)^{leg (H)} χ^{λ ∖ H} (ρ),

where

H

ranges over removable rim hooks of length

k

and

leg (H)

is one less than the number of rows occupied by

H

.

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