Generalizations of Chung-Feller Theorem
| dc.creator | Ma, Jun | |
| dc.creator | Yeh, Yeong-Nan | |
| dc.date | 2008-12-16 | |
| dc.date.accessioned | 2026-07-07T12:13:02Z | |
| dc.date.available | 2026-07-07T12:13:02Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0812.2978 | |
| dc.identifier | http://arxiv.org/abs/0812.2978 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210742 | |
| dc.subject | Combinatorics | |
| dc.title | Generalizations of Chung-Feller Theorem | |
| dc.type | text |