Amorphic association schemes with negative Latin square-type graphs |
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| Authors: | James A. Davis Qing Xiang |
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| Affiliation: | aDepartment of Mathematics and Computer Science, University of Richmond, Richmond, VA 23173, USA;bDepartment of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA |
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| Abstract: | Applying results from partial difference sets, quadratic forms, and recent results of Brouwer and Van Dam, we construct the first known amorphic association scheme with negative Latin square-type graphs and whose underlying set is a nonelementary abelian 2-group. We give a simple proof of a result of Hamilton that generalizes Brouwer's result. We use multiple distinct quadratic forms to construct amorphic association schemes with a large number of classes. |
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| Keywords: | Amorphic association scheme Association scheme Latin square-type partial difference set Negative Latin square-type partial difference set Partial difference set Quadratic form Quadric Strongly regular graph |
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