Geodesic
The number of solutions of \(X^ 2 = 0\) in triangular matrices over \(GF(q)\)
The electronic journal of combinatorics, Tome 3 (1996) no. 1
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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.
DOI : 10.37236/1226
Classification : 15A24
Mots-clés : quadratic matrix equation, triangular matrices 
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     author = {Shalosh B. Ekhad and Doron Zeilberger},
     title = {The number of solutions of {\(X^} 2 = 0\) in triangular matrices over {\(GF(q)\)}},
     journal = {The electronic journal of combinatorics},
     year = {1996},
     volume = {3},
     number = {1},
     doi = {10.37236/1226},
     zbl = {0851.15010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1226/}
}
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Shalosh B. Ekhad; Doron Zeilberger. The number of solutions of \(X^ 2 = 0\) in triangular matrices over \(GF(q)\). The electronic journal of combinatorics, Tome 3 (1996) no. 1. doi: 10.37236/1226

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