Restricted plane tree representations of four Motzkin-Catalan equations
نویسندگان
چکیده
منابع مشابه
From Motzkin to Catalan permutations
For every integer j¿1, we de ne a class of permutations in terms of certain forbidden subsequences. For j = 1, the corresponding permutations are counted by the Motzkin numbers, and for j =∞ (de ned in the text), they are counted by the Catalan numbers. Each value of j¿ 1 gives rise to a counting sequence that lies between the Motzkin and the Catalan numbers. We compute the generating function ...
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In this paper we introduce two new expansions for the generating functions of Catalan numbers and Motzkin numbers. The novelty of the expansions comes from writing the Taylor remainder as a functional of the generating function. We give combinatorial interpretations of the coefficients of these two expansions and derive several new results. These findings can be used to prove some old formulae ...
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Given a permutation σ ∈ Sn, one can partition the set {1, 2, . . . , n} into intervals A1, . . . , At such that σ(Aj) = Aj for every j. The restrictions of σ to the intervals in the finest of these decompositions are called connected components of σ. A permutation σ with a single connected component is called connected. Given a permutation σ ∈ Sn, we define the reverse of σ to be the permutatio...
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We prove various congruences for Catalan and Motzkin numbers as well as related sequences. The common thread is that all these sequences can be expressed in terms of binomial coefficients. Our techniques are combinatorial and algebraic: group actions, induction, and Lucas’ congruence for binomial coefficients come into play. A number of our results settle conjectures of Benoit Cloitre and Reinh...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1977
ISSN: 0095-8956
DOI: 10.1016/0095-8956(77)90003-x