K-NARAYANA SEQUENCE SELF-SIMILARITY

Engin Özkan , Bahar Kuloǧlu , James F Peters (1)

1 University of Manitoba [Winnipeg]

This paper introduces self-similarity inherent in planar Milich centered flip graphs derived from the Narayana sequence. We show that selfsimilarity 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. Contents 12 7. Expression of k n as a k-Narayana number 12 8. Catalan transform of the k-Narayana sequence 13 9. Hankel Transform 14 10. Conclusion 15 Appendix A. Cell Complexes 15 Appendix B. Shape Complexes 16 Appendix C. Finite 1-cycles and their Cyclic Group Presentation 17 References 19

Domaines: Combinatoire [math.CO]

Engin Özkan, Bahar Kuloǧlu, James F Peters. K-NARAYANA SEQUENCE SELF-SIMILARITY. 2021. ⟨hal-03242990⟩