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Article overview
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Generalizations of Chung-Feller Theorem | | Jun Ma
; Yeong-Nan Yeh
; | | Date: |
16 Dec 2008 | | Abstract: | The classical Chung-Feller theorem [2] tells us that the number of Dyck paths
of length $n$ with flaws $m$ is the $n$-th Catalan number and independent on
$m$. L. Shapiro [7] found the Chung-Feller properties for the Motzkin paths. In
this paper, we find the connections between these two Chung-Feller theorems. We
focus on the weighted versions of three classes of lattice paths and give the
generalizations of the above two theorems. We prove the Chung-Feller theorems
of Dyck type for these three classes of lattice paths and the Chung-Feller
theorems of Motzkin type for two of these three classes. From the obtained
results, we find an interesting fact that many lattice paths have the
Chung-Feller properties of both Dyck type and Motzkin type. | | Source: | arXiv, 0812.2978 | | Services: | Forum | Review | PDF | Favorites | |
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