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K-Narayana sequence self-Similarity. flip graph views of k-Narayana self-Similarity

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  • Özkan, Engin
  • Kuloǧlu, Bahar
  • Peters, James F.

Abstract

This paper introduces self-similarity inherent in planar Milich-Jennings centered flip graphs derived from the Narayana sequence. We show that self-similarity found in a Narayana sequence yields a connected spanning subgraph with a centered flip. This paper has several main results (1) Every Narayana sequence constructs a flip graph, (2) Every Narayana sequence is self-similar and (3) Every Pascal 3-triangle has a free group presentation.

Suggested Citation

  • Özkan, Engin & Kuloǧlu, Bahar & Peters, James F., 2021. "K-Narayana sequence self-Similarity. flip graph views of k-Narayana self-Similarity," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008274
    DOI: 10.1016/j.chaos.2021.111473
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    References listed on IDEAS

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    1. Stakhov, Alexey, 2007. "The generalized golden proportions, a new theory of real numbers, and ternary mirror-symmetrical arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 315-334.
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