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

作者： Shalosh B. Ekhad , Doron Zeilberger

关键词: Combinatorics 、 Discrete mathematics 、 Square (algebra) 、 Zero matrix 、 Mathematics 、 Triangular matrix

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