Previous Article in Journal
About Uniqueness of Steady Ricci Schwarzschild Solitons
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Combinatorial Identities for the Narayana Numbers

by
Ángel Plaza
1,*,† and
Steven J. Tedford
2,†
1
Department of Mathematics, University of Las Palmas de Gran Canaria, 35001 Las Palmas de Gran Canaria, Spain
2
Department of Mathematical Sciences, Misericordia University, 301 Lake St., Dallas, PA 18634, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Axioms 2025, 14(10), 771; https://doi.org/10.3390/axioms14100771
Submission received: 16 August 2025 / Revised: 13 October 2025 / Accepted: 16 October 2025 / Published: 17 October 2025

Abstract

We interpret the Narayana numbers combinatorially by having them count the number of tilings of an n-strip using squares and triominoes. Using this interpretation, we develop a collection of identities satisfied by the sequence of Narayana numbers. Additionally, these techniques are used to introduce the generalized Narayana numbers and the k-Narayana numbers and to prove corresponding identities.
Keywords: Narayana numbers; combinatorial identities; genreralized Narayana numbers; k-Narayana numbers Narayana numbers; combinatorial identities; genreralized Narayana numbers; k-Narayana numbers

Share and Cite

MDPI and ACS Style

Plaza, Á.; Tedford, S.J. Combinatorial Identities for the Narayana Numbers. Axioms 2025, 14, 771. https://doi.org/10.3390/axioms14100771

AMA Style

Plaza Á, Tedford SJ. Combinatorial Identities for the Narayana Numbers. Axioms. 2025; 14(10):771. https://doi.org/10.3390/axioms14100771

Chicago/Turabian Style

Plaza, Ángel, and Steven J. Tedford. 2025. "Combinatorial Identities for the Narayana Numbers" Axioms 14, no. 10: 771. https://doi.org/10.3390/axioms14100771

APA Style

Plaza, Á., & Tedford, S. J. (2025). Combinatorial Identities for the Narayana Numbers. Axioms, 14(10), 771. https://doi.org/10.3390/axioms14100771

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop