• 한국수학사학회지
• /
• 제34권3호
• /
• pp.113-115
• /
• 2021

An elementary proof of the Catalan Theorem is given.

• East Asian mathematical journal
• /
• 제39권1호
• /
• pp.23-27
• /
• 2023

In this paper, we derive the some identities which are related to the multifactorial numbers and the Catalan numbers. We utilize the fundamental theorem of Riordan matrix to obtain those identities.

• 대한수학회논문집
• /
• 제13권2호
• /
• pp.435-443
• /
• 1998

Some mathematical constants have been used in evaluating series involving the Zeta function, the origin of which can be traced back to an over two centries old theorem of Christian Goldbach. We show some of the series involving the Zeta function can be evaluated in terms of the Catalan's constant by using the theory of the double Gamma function.

• 호남수학학술지
• /
• 제43권4호
• /
• pp.641-653
• /
• 2021

Armstrong enumerated the number of Fuss-Catalan paths with a given type and Rhoades provided the number of Dyck paths with a given type and a given number of blocks. In this paper we generalize those results to enumerate the number of Fuss-Catalan paths with a fixed type and a fixed number of blocks. We provide two proofs of this result. The first one uses the Chung-Feller theorem and a certain polynomial, while the second one is bijective. Also, we give a conjecture generalizing this result to the family of small Fuss-Schröder paths.