In this paper, a symplectic fission scheme for the association scheme of $ m\times n $ rectangular matrices over the finite field $ \mathbb{F}_q $, denoted by $ {\rm{SMat}}(m\times n, q) $, is constructed, where $ q $ is a power of a prime number. We discuss its association classes and inner automorphism group. In particular, we determine the intersection numbers and automorphism group of $ {\rm{SMat}}(m\times n, q) $ for $ m = 1 $ and $ m = 2 $.
Citation: Yang Zhang, Shuxia Liu, Liwei Zeng. A symplectic fission scheme for the association scheme of rectangular matrices and its automorphisms[J]. AIMS Mathematics, 2024, 9(11): 32819-32830. doi: 10.3934/math.20241570
In this paper, a symplectic fission scheme for the association scheme of $ m\times n $ rectangular matrices over the finite field $ \mathbb{F}_q $, denoted by $ {\rm{SMat}}(m\times n, q) $, is constructed, where $ q $ is a power of a prime number. We discuss its association classes and inner automorphism group. In particular, we determine the intersection numbers and automorphism group of $ {\rm{SMat}}(m\times n, q) $ for $ m = 1 $ and $ m = 2 $.
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Yang Zhang, Shuxia Liu, Liwei Zeng. A symplectic fission scheme for the association scheme of rectangular matrices and its automorphisms[J]. AIMS Mathematics, 2024, 9(11): 32819-32830. doi: 10.3934/math.20241570
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