The Number of Solutions of $X^2=0$ in Triangular Matrices Over $GF(q)$

Shalosh B. Ekhad, Doron Zeilberger

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.


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