On the p′-Subgraph of the Young Graph

Abstract

Let p be a prime number. In this article we study the restriction to 𝔖n−1$$\mathfrak {S}{n-1}$$ of irreducible characters of degree coprime to p of 𝔖n$$\mathfrak {S}{n}$$. In particular, we study the combinatorial properties of the subgraph 𝕐p′$$\mathbb {Y}_{p^{\prime }}$$ of the Young graph 𝕐$$\mathbb {Y}$$. This is an extension to odd primes of the work done in Ayyer et al. (2016) for p = 2.