This paper presents a simple approach to invert the matrix P n + I n by applying the Euler polynomials and Bernoulli numbers, where P n is the Pascal matrix.

Several important combinatorial arrays, after inserting some minus signs, turn out to be involutions when considered as lower triangular matrices. Among these are the Pascal, RNA, and directed animal matrices. These examples and many others are in the Bell subgroup of the Riordan group. We characterize all such pseudo-involutions by means of a single sequence called the ∆-sequence. Finally we c...

In this paper we extend some results on the factorization of matrices associated to Lucas, Pascal, Stirling sequences by the Fibonacci matrix. We provide explicit factorizations of any matrix by the matrix associated with an r-order recurrent sequence Un (having U0 = 0). The Cholesky factorization for the symmetric matrix associated to Un is also obtained.

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...