On a Remarkable Sequence of Polynomials
On a Remarkable Sequence of Polynomials
Séminaires et Congrès | 1997
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- Année : 1997
- Tome : 2
- Format : Papier
- Langue de l'ouvrage :
Anglais - Class. Math. : 15A57, 22E25, 05A15
- Pages : 35-42
A remarkable sequence of polynomials is considered. These polynomials in $q$ describe in particular the number of solution to the equation $X^2=0$ in triangular $n \times n$ matrices over a field ${\Bbb F}_q$ with $q$ elements. They have at least three other important interpretations and a conjectural explicit expression in terms of the entries of the Catalan triangle.