Refined Chung-Feller theorems for lattice paths

Authors:
Sen-Peng Eu;Tung-Shan Fu;Yeong-Nan Yeh
Affiliations:
Department of Applied Mathematics, National University of Kaohsiung, Taiwan, ROC;Mathematics Faculty, National Pingtang Institute of Commerce, Pingtang, Taiwan, ROC;Institute of Mathematics, Academia Sinica, Taipei, Taiwan, ROC
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

Citing 4
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Abstract

In this paper we prove a strengthening of the classical Chung-Feller theorem and a weighted version for Schröder 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 schröder paths with flaws.