Work

Tiling Models for Palindromic and n ‐Colored Compositions With 1 s and 3 s

Year: 2026

Type: article

Abstract: In this work, we explore compositions of positive integers into parts consisting of 1 and 3 s, highlighting their close connection to the Narayana numbers. We also examine palindromic compositions of this type and introduce arithmetic functions that reflect their structural properties. Furthermore, the Woon and PI tree structures related to the Narayana numbers are constructed and visually illustrated. To provide an intuitive understanding, we present tiling models corresponding to these compositions and use them to derive a variety of combinatorial identities. Moreover, we extend our approach to tiling models associated with Narayana polynomials, establishing additional identities through this framework. We also introduce an n ‐color extension of these compositions, exploring how the additional coloring dimension affects their combinatorial properties. Finally, we consider compositions with 1 and 3 s and derive several related identities that further illustrate their relationship with the Narayana numbers.

Source: Journal of Mathematics

DOI: 10.1155/jom/6335538

Authors: Orhan Dişkaya, Bahar Kuloğlu, Hayrullah Özimamoğlu, Ahmet Kaya, Hamza Menken

Institutions: Mersin Üniversitesi, Sivas Bilim ve Teknoloji Üniversitesi, Nevşehir Hacı Bektaş Veli University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,160

Funder: Türkiye Bilimsel ve Teknolojik Araştırma Kurumu