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Refined ChungFeller Theorems for Lattice Paths
"... In this paper we prove a strengthening of the classical ChungFeller 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 b ..."
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Cited by 11 (3 self)
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In this paper we prove a strengthening of the classical ChungFeller 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
Generalizations of ChungFeller theorem
 European J. Combin
, 2011
"... In this paper, we develop a method to find ChungFeller extensions for three kinds of different rooted lattice paths and prove ChungFeller 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 interp ..."
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Cited by 5 (2 self)
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In this paper, we develop a method to find ChungFeller extensions for three kinds of different rooted lattice paths and prove ChungFeller 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
Generalizations of The ChungFeller Theorem
, 812
"... The classical ChungFeller theorem [2] tells us that the number of Dyck paths of length n with flaws m is the nth Catalan number and independent on m. L. Shapiro [7] found the ChungFeller properties for the Motzkin paths. In this paper, we find the connections between these two ChungFeller theore ..."
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theorems. We focus on the weighted versions of three classes of lattice paths and give the generalizations of the above two theorems. We prove the ChungFeller theorems of Dyck type for these three classes of lattice paths and the ChungFeller theorems of Motzkin type for two of these three classes. From
Generalizations of The ChungFeller Theorem II
, 903
"... The classical ChungFeller theorem [2] tells us that the number of Dyck paths of length n with m flaws is the nth Catalan number and independent on m. L. Shapiro [9] found the ChungFeller properties for the Motzkin paths. Mohanty’s book [5] devotes an entire section to exploring ChungFeller theor ..."
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theorem. Many ChungFeller 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 nonpositive length and the rightmost minimum length. We obtain the ChungFeller theorems of the (n, m)lattice path
Generalizations of The ChungFeller Theorem Jun Ma a,∗
"... The classical ChungFeller theorem [2] tells us that the number of Dyck paths of length n with m flaws is the nth Catalan number and independent on m. L. Shapiro [9] found the ChungFeller properties for the Motzkin paths. In this paper, we find the connections between these two ChungFeller theore ..."
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theorems. We focus on the weighted versions of three classes of lattice paths and give the generalizations of the above two theorems. We prove the ChungFeller theorems of Dyck type for these three classes of lattice paths and the ChungFeller theorems of Motzkin type for two of these three classes. From
Strings of length 3 in GrandDyck paths and the ChungFeller property
"... This paper deals with the enumeration of GrandDyck 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 ChungFeller theorem are obtained. 1 ..."
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Cited by 1 (0 self)
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This paper deals with the enumeration of GrandDyck 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 ChungFeller theorem are obtained. 1
AN INVESTIGATION OF THE CHUNGFELLER THEOREM
, 2004
"... Abstract. In this paper, we shall prove the ChungFeller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin [2]. 1. ..."
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Abstract. In this paper, we shall prove the ChungFeller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin [2]. 1.
ChungFeller property in view of generating functions
 Electron. J. Combin
"... The classical ChungFeller Theorem offers an elegant perspective for enumerating the Catalan number cn = 1 2n) n+1 n. One of the various proofs is by the uniformpartition method. The method shows that the set of the free Dyck npaths, which have ( 2n) n in total, is uniformly partitioned into n + 1 ..."
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Cited by 2 (1 self)
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The classical ChungFeller Theorem offers an elegant perspective for enumerating the Catalan number cn = 1 2n) n+1 n. One of the various proofs is by the uniformpartition method. The method shows that the set of the free Dyck npaths, which have ( 2n) n in total, is uniformly partitioned into n + 1
Counterexampleguided Abstraction Refinement
, 2000
"... We present an automatic iterative abstractionrefinement methodology in which the initial abstract model is generated by an automatic analysis of the control structures in the program to be verified. Abstract models may admit erroneous (or "spurious") counterexamples. We devise new symb ..."
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Cited by 848 (71 self)
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We present an automatic iterative abstractionrefinement methodology in which the initial abstract model is generated by an automatic analysis of the control structures in the program to be verified. Abstract models may admit erroneous (or "spurious") counterexamples. We devise new
Results 1  10
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