A Decomposition Algorithm for Noncrossing Trees
نویسندگان
چکیده
منابع مشابه
A Decomposition Algorithm for Noncrossing Trees
Based on the classic bijective algorithm for trees due to Chen, we present a decomposition algorithm for noncrossing trees. This leads to a combinatorial interpretation of a formula on noncrossing trees of size n with k descents. We also derive the formula for noncrossing trees of size n with k descents and i leaves, which is a refinement of the formula given by Flajolet and Noy. As an applicat...
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Abstract. We give a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation of a formula on noncrossing trees and symmetric ternary trees in answer to a problem proposed by Hough. We use the representation of Panholzer and Prodinger for noncrossing trees and find a correspondence between a class of noncrossing trees, called proper noncrossing trees, and the...
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We define an orientation on the edges of a noncrossing tree induced by the labels: for a noncrossing tree (i.e., the edges do not cross) with vertices 1, 2, . . . , n arranged on a circle in this order, all edges are oriented towards the vertex whose label is higher. The main purpose of this paper is to study the distribution of noncrossing trees with respect to the indegree and outdegree seque...
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We give a simple and natural proof of (an extension of) the identity P (k, l, n) = P2(k − 1, l − 1, n − 1). The number P (k, l, n) counts noncrossing partitions of {1, 2, . . . , l} into n parts such that no part contains two numbers x and y, 0 < y − x < k. The lower index 2 indicates partitions with no part of size three or more. We use the identity to give quick proofs of the closed formulae ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/3353