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An Explicit Formula for the Number of Solutions of X^2=0 in Triangular Matrices over a Finite Field

Shalosh B. Ekhad·Doron Zeilberger
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Abstract

We prove an explicit formula for the number of $n \times n$ upper triangular matrices, over $GF(q)$, whose square is the zero matrix. This formula was recently conjectured by Sasha Kirillov and Anna Melnikov[KM].

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Shalosh B. Ekhad, Doron Zeilberger. 1995-12-19. An Explicit Formula for the Number of Solutions of X^2=0 in Triangular Matrices over a Finite Field. https://arxiv.org/abs/math/9512224

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