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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153015We 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].Plain TeXCombinatoricsAn Explicit Formula for the Number of Solutions of X^2=0 in Triangular Matrices over a Finite Fieldtext