A very general binomial matrix

Leo Betthauser, Ömür Deveci and Josh Hiller
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 125—133
DOI: 10.7546/nntdm.2021.27.1.125-133
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Authors and affiliations

Leo Betthauser
Department of Mathematics, PO Box 118105, University of Florida
Gainesville, FL 32611-8105, United States

Ömür Deveci
Department of Mathematics, Faculty of Science and Letters, Kafkas University
36100, Turkey

Josh Hiller
Department of Mathematics and Computer Science, Adelphi University
New York, United States

Abstract

We define the very general binomial matrix and find its eigendecomposition over arbitrary rings when such a decomposition is possible. Using this decomposition, we are able to compute the order of several varieties of Pascal’s matrices.

Keywords

  • Pascal’s matrix
  • Binomial coefficients
  • Matrix

2010 Mathematics Subject Classification

  • 11B65
  • 15A09
  • 15A16

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Cite this paper

Betthauser, L., Deveci, Ö., & Hiller, J. (2021). A very general binomial matrix. Notes on Number Theory and Discrete Mathematics, 27(1), 125-133, doi: 10.7546/nntdm.2021.27.1.125-133.

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