Abstract
A Pascal matrix function is introduced by Call and Velleman (1993). A decomposition of Stirling matrices of the rst kind and the second kind by using the Pascal matrix function is given by Cheon and Kim (2001). In this paper, we introduce shift Stirling matrices and their decompositions by using the Pascal matrix.Finally, we extend our discussion to generalized Stirling numbers and their matrices, which were studied by He (2013), and Hsu and Shiue (1998). Matrix equations presented in this article re ect the relationships between the rst kind, the second kind, and generalized Stirling numbers and the binomial numbers. The expressions are succinct and helpful to nd more properties of Stirling numbers.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
