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Abstract for Shalosh B. Ekhad and Doron Zeilberger, The Number of Solutions of $X^2=0$ in Triangular Matrices Over $GF(q)$

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.

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