<?xml version="1.0" encoding="UTF-8"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-10-19T01:09:12Z</responseDate><request verb="GetRecord" identifier="oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/13198" metadataPrefix="oai_dc">https://ebyu-rdlopen.rawdatalibrary.net/oai/request</request><GetRecord><record><header><identifier>oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/13198</identifier><datestamp>2026-10-18T20:43:13Z</datestamp><setSpec>openaire</setSpec><setSpec>driver</setSpec><setSpec>com_ebyu_10000</setSpec><setSpec>col_ebyu_10001</setSpec></header><metadata><oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><dc:title>K-Narayana sequence self-Similarity. flip graph views of k-Narayana self-Similarity</dc:title><dc:creator>Özkan, Engin</dc:creator><dc:creator>Kuloǧlu, Bahar</dc:creator><dc:creator>Peters, James F.</dc:creator><dc:subject>Flip graphs</dc:subject><dc:subject>K-Narayana sequence</dc:subject><dc:subject>Pascal 3-triangle</dc:subject><dc:subject>Planar graph</dc:subject><dc:subject>Self-Similarity</dc:subject><dc:subject>Flip graph</dc:subject><dc:subject>Free groups</dc:subject><dc:subject>Group presentation</dc:subject><dc:subject>K-narayanum sequence</dc:subject><dc:subject>Self-similar</dc:subject><dc:subject>Self-similarities</dc:subject><dc:subject>Spanning subgraphs</dc:subject><dc:subject>Graphic methods</dc:subject><dc:description>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. © 2021</dc:description><dc:publisher>Elsevier Ltd</dc:publisher><dc:date>2021</dc:date><dc:type>Article</dc:type><dc:identifier>https://rdlopen.rawdatalibrary.net/r/ebyu/13198</dc:identifier><dc:identifier>https://doi.org/10.1016/j.chaos.2021.111473</dc:identifier><dc:identifier>0960-0779</dc:identifier><dc:language>en</dc:language><dc:relation>Chaos, Solitons and Fractals</dc:relation><dc:rights>info:eu-repo/semantics/openAccess</dc:rights><dc:type>info:eu-repo/semantics/article</dc:type><dc:identifier>https://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/13198</dc:identifier></oai_dc:dc></metadata></record></GetRecord></OAI-PMH>