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The k‐Augmented Pascal Matrix and Its Properties

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  • Gonca Kizilaslan
  • Taekyun Kim

Abstract

We define the k‐augmented Pascal matrix and present both a generalization and an alternative version of this matrix. We derive some properties of the defined matrices and establish a connection with generalized Stirling numbers and second‐order Eulerian numbers. Additionally, we provide a factorization of the k‐augmented Pascal matrix, highlighting its connection to the Fibonacci matrix.

Suggested Citation

  • Gonca Kizilaslan & Taekyun Kim, 2025. "The k‐Augmented Pascal Matrix and Its Properties," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:6280240
    DOI: 10.1155/jom/6280240
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    References listed on IDEAS

    as
    1. Kim, Dae San & Kim, Taekyun, 2015. "A matrix approach to some identities involving Sheffer polynomial sequences," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 83-101.
    2. Gonca Kizilaslan, 2025. "Pascal-like matrix with double factorial binomial coefficients," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 499-511, June.
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