Generalizations of Chung-Feller Theorem II
| dc.creator | Ma, Jun | |
| dc.creator | Yeh, Yeong-nan | |
| dc.date | 2009-03-04 | |
| dc.date.accessioned | 2026-07-07T12:49:00Z | |
| dc.date.available | 2026-07-07T12:49:00Z | |
| dc.description | The classical Chung-Feller theorem [2] tells us that the number of Dyck paths of length $n$ with $m$ flaws is the $n$-th Catalan number and independent on $m$. L. Shapiro [9] found the Chung-Feller properties for the Motzkin paths. Mohanty's book [5] devotes an entire section to exploring Chung-Feller theorem. Many Chung-Feller theorems are consequences of the results in [5]. In this paper, we consider the $(n,m)$-lattice paths. We study two parameters for an $(n,m)$-lattice path: the non-positive length and the rightmost minimum length. We obtain the Chung-Feller theorems of the $(n,m)$-lattice path on these two parameters by bijection methods. We are more interested in the pointed $(n,m)$-lattice paths. We investigate two parameters for an pointed $(n,m)$-lattice path: the pointed non-positive length and the pointed rightmost minimum length. We generalize the results in [5]. Using the main results in this paper, we may find the Chung-Feller theorems of many different lattice paths. | |
| dc.identifier | https://arxiv.org/abs/0903.0705 | |
| dc.identifier | http://arxiv.org/abs/0903.0705 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222252 | |
| dc.subject | Combinatorics | |
| dc.title | Generalizations of Chung-Feller Theorem II | |
| dc.type | text |