Evaluations of some determinants of matrices related to the Pascal triangle

Details Evaluations of some determinants of matrices related to the Pascal triangle Evaluations of some determinants of matrices related to the Pascal triangle

2001-11-30

arxiv.org/abs/math/0111328v1

S\'eminaire Lotharingien Combin. 47 (2002), Article B47g, 19 pp.

Mathematics

Combinatorics

19 pages, AmS-TeX

Scientific paper

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

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