@article{b990a8019c634fda8772e8c7c3522cf0,
title = "Refined Chung-Feller theorems for lattice paths",
abstract = "In this paper we prove a strengthening of the classical Chung-Feller theorem and a weighted version for Schr{\"o}der paths. Both results are proved by refined bijections which are developed from the study of Taylor expansions of generating functions. By the same technique, we establish variants of the bijections for Catalan paths of order d and certain families of Motzkin paths. Moreover, we obtain a neat formula for enumerating Schr{\"o}der paths with flaws.",
keywords = "Catalan paths, Chung-Feller theorem, Generating function, Motzkin paths, Schr{\"o}der paths, Taylor expansion",
author = "Eu, {Sen Peng} and Fu, {Tung Shan} and Yeh, {Yeong Nan}",
note = "Funding Information: E-mail addresses: speu@nuk.edu.tw (S.-P. Eu) , tsfu@npic.edu.tw (T.-S. Fu) , mayeh@math.sinica.edu.tw (Y.-N. Yeh) . 1 Partially supported by National Science Council, Taiwan, R.O.C. (NSC 92-2119-M-390-001). 2 Partially supported by National Science Council, Taiwan, R.O.C. (NSC 92-2115-M-251-001). 3 Partially supported by National Science Council, Taiwan, R.O.C. (NSC 92-2115-M-001-016).",
year = "2005",
month = oct,
doi = "10.1016/j.jcta.2004.11.016",
language = "English",
volume = "112",
pages = "143--162",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
number = "1",
}