This paper presents some relationships between Pascal matrices, Stirling numbers, and Bernouilli numbers.
Symmetric polynomials, Pascal matrices, and Stirling matrices
โ Scribed by Michael Z. Spivey; Andrew M. Zimmer
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 132 KB
- Volume
- 428
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
This paper contains a general characterization for the permutation polynomials of the symmetric matrices over any ยฎeld. Speciยฎc characterizations are for symmetric matrices over algebraically closed ยฎelds, principal axis ยฎelds, and ยฎnite ยฎelds. In the latter case enumeration formulas are established
The topic of the paper is spectral factorization of rectangular and possibly non-full-rank polynomial matrices. To each polynomial matrix we associate a matrix pencil by direct assignment of the coefficients. The associated matrix pencil has its finite generalized eigenvalues equal to the zeros of t
We use basic properties of infinite lower triangular matrices and the connections of Toeplitz matrices with generating-functions to obtain inversion formulas for several types of q-Pascal matrices, determinantal representations for polynomial sequences, and identities involving the q-Gaussian coeffi