Symmetric Polynomials, Pascal Matrices, and Stirling Matrices
Linear Algebra and its Applications
Mathematics and Computer Science
We consider lower-triangular matrices consisting of symmetric polynomials, and we show how to factorize and invert them. Since binomial coefficients and Stirling numbers can be represented in terms of symmetric polynomials, these results contain factorizations and inverses of Pascal and Stirling matrices as special cases. This work generalizes that of several other authors on Pascal and Stirling matrices.
Spivey, Michael Z., and Andrew M. Zimmer. 2008. "Symmetric polynomials, Pascal matrices, and Stirling matrices." Linear Algebra And Its Applications 428(4): 1127-1134.