Determinants of matrices related to the Pascal triangle
نویسندگان
چکیده
منابع مشابه
Matrices Related to the Pascal Triangle
for 0 ≤ i, j ∈ N. The matrix P is hence the famous Pascal triangle yielding the binomial coefficients and can be recursively constructed by the rules p0,i = pi,0 = 1 for i ≥ 0 and pi,j = pi−1,j + pi,j−1 for 1 ≤ i, j. In this paper we are interested in (sequences of determinants of finite) matrices related to P . The present section deals with some minors (determinants of submatrices) of the abo...
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for 0 ≤ i, j ∈ N. The matrix P is hence the famous Pascal triangle yielding the binomial coefficients and can be recursively constructed by the rules p0,i = pi,0 = 1 for i ≥ 0 and pi,j = pi−1,j + pi,j−1 for 1 ≤ i, j. In this paper we are interested in (sequences of determinants of finite) matrices related to P . The present section deals with determinants of some minors of the above Pascal tria...
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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 14 (2002), to appear].
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2002
ISSN: 1246-7405
DOI: 10.5802/jtnb.344