Faculty Of Computer And Mathematical Science

This project is all about a survey of Fine numbers which is intimately related to the Catalan numbers. Two manifestations are the identity and the generating function identities rnThe project also gives a unified presentation and history of the so previous results in the literature that mentioned the Fine numbers. rnAmong the settings that mention the occurrences of the Fine numbers, Dyck paths, Ordered trees, Paths, Path pairs and non-crossing partitions are some of them that will be discussed in section 2 of the paper with full fledged explanation. rn And finally the last section, section three presents the statistic relationship between Fine paths an d Dyck paths using both Ordinary and Bivariate generating functions

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