The linear algebra of the r-Whitney matrices

Abstract

The linear algebraic theory of the Pascal and Vandermonde matrix is well developed by many authors. In the last two decades many interrelations have been discovered between the mentioned matrices, their generalizations and the Stirling matrices. We follow this direction and discover new matricial relations by using the so-called r-Whitney numbers. Along this way, we develop two natural extensions of the Vandermonde matrix with which we can study and evaluate successive power sums of arithmetic progressions and win new identities for the r-Whitney numbers.

Keywords:

• r-Whitney number
• r-Whitney matrix
• combinatorial identities
• Pascal matrix

2010 Mathematics Subject Classification::

• Primary: 11B73
• Secondary: 15A15
• 15A23

Acknowledgments

The first author thanks for the invitation to Bogotá where the mayor part of this paper was born.

Funding

The research of István Mező was supported by the Scientific Research Foundation of Nanjing University of Information Science & Technology, and The Startup Foundation for Introducing Talent of NUIST. Project no.: S8113062001. The research of José L. Ramírez was partially supported by Universidad Sergio Arboleda [grant no. DII-262].