Séminaire Lotharingien de Combinatoire, B47g (2002), 19 pp.
Evaluations of Some Determinants of Matrices
Related to the Pascal Triangle
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
Théorie Nombres Bordeaux 14 (2002), 19-41].
Received: January 12, 2002; Accepted: February 19, 2002; Final Version:
March 25, 2002.
The following versions are available:
Comment by the author: It is much easier to prove Theorem 4 by
appealing to (the more general) Proposition 1 in the author's paper
"Advanced Determinant Calculus,"
Séminaire Lotharingien Combin.
42 ("The Andrews
Festschrift") (1999), Article B42q, 67 pp.