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, 2024)
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.