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Chung-Feller Property in View of Generating Functions

2011
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Electronic Journal of Combinatorics
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The classical Chung-Feller Theorem offers an elegant perspective for enumerating the Catalan number $c_n= \frac{1}{n+1}\binom{2n}{n}$. One of the various proofs is by the uniform-partition method. The method shows that the set of the free Dyck $n$-paths, which have $\binom{2n}{n}$ in total, is uniformly partitioned into $n+1$ blocks, and the ordinary Dyck $n$-paths form one of these blocks; therefore the cardinality of each block is $\frac{1}{n+1}\binom{2n}{n}$. In this article, we study the

doi:10.37236/591
fatcat:i6gvk6g6bff6pbbysads325zke