Evaluations of some determinants of matrices related to the Pascal triangle

الأصل · EN

We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence aᵢ,ⱼ=aᵢ₋₁,ⱼ+aᵢ,ⱼ₋₁, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Théorie Nombres Bordeaux 13 (2001), to appear; see http://arxiv.org/abs/math.CO/0109013].