Asymptotics of the number of involutions in finite classical groups

2016/02/11 by Fulman, Jason, Guralnick, Robert, Stanton, Dennis · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1602.03611

Abstract

Answering a question of Geoff Robinson, we compute the large n limiting proportion of i(n,q)/q^[n²/2], where i(n,q) denotes the number of involutions in GL(n,q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new "sum=product" identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.

Cited by

• Asymptotics for the enumeration of commuting matrices over finite fields

Related

• On involutions and indicators of finite orthogonal groups
• Finite groups with many involutions
• A counterexample to Herzog's Conjecture on the number of involutions
• The involution width of finite simple groups
• The asymptotics of monotone subsequences of involutions