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 of irreducible characters of degree coprime to p of Sn. In particular, we study the combinatorial properties of the subgraph Y p ′ of the Young graph Y. This is an extension to odd primes of the work done in [1] for p = 2.

Hook removal operators on the odd Young graph

“…On the other hand a 2 ℓ -abacus for f 0 (λ) can be obtained from A by sliding a bead c ′ in position (i, b 0 ) of A to position (i, b 0 − 1). This follows from Lemma 3.1(3) because w 2 ℓ (A(1, ← c ′ )) = w 2 ℓ (A) (by direct verification, or more generally by [8,Lemma 2.5]) and (A(1, ← c ′ )) ↑ = B 0 . We call A 0 := A(1, ← c ′ ).…”

“…Let n = 12 = 2 3 + 2 2 and take k = 1. The cycle type of ω 12,2 is (8,2,2). Let λ = (10, 1 2 ) ⊢ o 12.…”

On the Aα-Spectral Radii of Cactus Graphs

“…In the mathematical literature, there are numerous studies of properties of the (signless, A α ) spectral radius [2][3][4][5][6][7]. For instance, Chen [8] explored properties of spectra of graphs and line graphs.…”