Chung-Feller Property in View of Generating Functions
نویسندگان
چکیده
منابع مشابه
Chung-Feller Property in View of Generating Functions
The classical Chung-Feller Theorem offers an elegant perspective for enumerating the Catalan number cn = 1 n+1 ( 2n n ) . One of the various proofs is by the uniformpartition method. The method shows that the set of the free Dyck n-paths, which have ( 2n n ) in total, is uniformly partitioned into n + 1 blocks, and the ordinary Dyck n-paths form one of these blocks; therefore the cardinality of...
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Large Schröder paths, sparse noncrossing partitions, partial horizontal strips, and 132-avoiding alternating sign matrices are objects enumerated by Schröder numbers. In this paper we give formula for the number of Schröder objects with given type and number of connected components. The proofs are bijective using ChungFeller style. A bijective proof for the number of Schröder objects with given...
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In this paper, we develop a method to find Chung-Feller extensions for three kinds of different rooted lattice paths and prove Chung-Feller theorems for such lattice paths. In particular, we compute a generating function S(z) of a sequence formed by rooted lattice paths. We give combinatorial interpretations to the function of Chung-Feller type S(z)−yS(yz) 1−y for the generating function S(z). ...
متن کاملGeneralizations of The Chung-Feller Theorem II
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...
متن کاملGeneralizations of The Chung-Feller Theorem
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 generalizati...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/591