The Relation of Noncrossing Partitioning of Odd and Even Numbers with Catalan Numbers
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Abstract
Catalan numbers, denoted by Cn, are generally defined by the equation Cn = 1/(n+1) (2n
n) with n ≥ 0 and n ∈ ℤ. Catalan numbers have forms that can be determined through general
and recursive forms. Catalan numbers have several applications to various combinatorial
problems, such as in recursive analysis and the application of combinatorial theory to
partitions that can form Catalan numbers. The odd numbers are defined as integers that are
not divisible by two, expressed in the form {2k + 1; k ∈ ℤ} . Meanwhile, even numbers are
defined as integers that are divisible by two, expressed in the form {2k; k ∈ ℤ} . In this study
we discuss the noncrossing partitions of positive odd numbers and positive even numbers.
The results show those the noncrossing partitions have relationship with Catalan numbers.
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