A semi-recursion for the number of involutions in special orthogonal groups over finite fields |
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| Authors: | Feiqi Jiang C. Ryan Vinroot |
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| Affiliation: | aDepartment of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109, United States;bDepartment of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187, United States |
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| Abstract: | Let I(n) be the number of involutions in a special orthogonal group 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) form a semi-recursion, in that for m>1 we haveI(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 Fq. |
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| Keywords: | MSC: 05A19 05A30 20G40 |
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