Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583088 | Finite Fields and Their Applications | 2011 | 20 Pages |
Abstract
Let I(n)I(n) be the number of involutions in a special orthogonal group SO(n,Fq)SO(n,Fq) defined over a finite field with q elements, where q is the power of an odd prime. Then the numbers I(n)I(n) form a semi-recursion, in that for m>1m>1 we haveI(2m+3)=(q2m+2+1)I(2m+1)+q2m(q2m−1)I(2m−2).I(2m+3)=(q2m+2+1)I(2m+1)+q2m(q2m−1)I(2m−2). We give a purely combinatorial proof of this result, and we apply it to give a universal bound for the character degree sum for finite classical groups defined over FqFq.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Feiqi Jiang, C. Ryan Vinroot,