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All Journal Integra: Journal of Integrated Mathematics and Computer Science
Amansyah, Wahyu Dwi
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Computer Science & IT Mathematics

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The Relation of Noncrossing Partitioning of Odd and Even Numbers with Catalan Numbers Amansyah, Wahyu Dwi; Wamiliana; Hamzah, Nur
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 1 (2024): March
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.2024114

Abstract

Catalan numbers, denoted by Cn, are generally defined by the equation Cn = 1/(n+1) (2nn) with n ≥ 0 and n ∈ ℤ. Catalan numbers have forms that can be determined through generaland recursive forms. Catalan numbers have several applications to various combinatorialproblems, such as in recursive analysis and the application of combinatorial theory topartitions that can form Catalan numbers. The odd numbers are defined as integers that arenot divisible by two, expressed in the form {2k + 1; k ∈ ℤ} . Meanwhile, even numbers aredefined as integers that are divisible by two, expressed in the form {2k; k ∈ ℤ} . In this studywe discuss the noncrossing partitions of positive odd numbers and positive even numbers.The results show those the noncrossing partitions have relationship with Catalan numbers.
Co-Authors Nur Hamzah Wamiliana