Generation of Pascal Triangle Using Matrices
نویسندگان
چکیده
منابع مشابه
1 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 determinants of some minors of the above Pascal tria...
متن کاملMatrices 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...
متن کاملPascal Matrices
Every polynomial of degree n has n roots; every continuous function on [0, 1] attains its maximum; every real symmetric matrix has a complete set of orthonormal eigenvectors. “General theorems” are a big part of the mathematics we know. We can hardly resist the urge to generalize further! Remove hypotheses, make the theorem tighter and more difficult, include more functions, move into Hilbert s...
متن کاملEvaluations 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 [J. Théorie Nombres Bordeaux 14 (2002), to appear].
متن کاملA Pascal-Type Triangle Characterizing Twin Primes
It is the purpose of this article to present a triangular array of numbers similar to Pascal’s triangle and to prove a corresponding criterion for the twin prime pairs. A further goal is to place all this in the context of some classical orthogonal polynomials and to relate it to some recent work of John D’Angelo. To begin, and for the sake of completeness, we present a short proof of the Pasca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Linear Algebra & Matrix Theory
سال: 2017
ISSN: 2165-333X,2165-3348
DOI: 10.4236/alamt.2017.74008