Strings of Length 3 in Grand-Dyck Paths and the Chung-Feller Property
نویسندگان
چکیده
This paper deals with the enumeration of Grand-Dyck paths according to the statistic “number of occurrences of τ” for every string τ of length 3, taking into account the number of flaws of the path. Consequently, some new refinements of the Chung-Feller theorem are obtained.
منابع مشابه
Generalizations 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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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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عنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012