D ec 1 99 5 An Explicit Formula for the Number of Solutions of X 2 = 0 in Triangular Matrices Over a Finite Field
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چکیده
X iv :m at h/ 95 12 22 4v 1 [ m at h. C O ] 1 9 D ec 1 99 5 An Explicit Formula for the Number of Solutions of X = 0 in Triangular Matrices Over a Finite Field Shalosh B. EKHAD and Doron ZEILBERGER Abstract: We prove an explicit formula for the number of n × n upper triangular matrices, over GF (q), whose square is the zero matrix. This formula was recently conjectured by Sasha Kirillov and Anna Melnikov[KM]. Theorem: The number of n × n upper-triangular matrices over GF (q) (the finite field with q elements), whose square is the zero matrix, is given by the polynomial Cn(q), where, C2n(q) = ∑
منابع مشابه
The Number of Solutions of X^2=0 in Triangular Matrices Over GF(q)
We prove an explicit formula for the number of n × n upper triangular matrices, over GF (q), whose square is the zero matrix. Theorem. The number of n × n upper-triangular matrices over GF (q) (the finite field with q elements), whose square is the zero matrix, is given by the polynomial C n (q), where, C 2n (q) = j 2n n − 3j − 2n n − 3j − 1 · q n 2 −3j 2 −j , C 2n+1 (q) = j 2n + 1 n − 3j − 2n ...
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