Bilabelled increasing trees and hook-length formulae
نویسندگان
چکیده
منابع مشابه
Bilabelled increasing trees and hook-length formulae
We introduce two different kind of increasing bilabellings of trees, for which we provide enumeration formulæ. One of the bilabelled tree families considered is enumerated by the reduced tangent numbers and is in bijection with a tree family introduced by Poupard [11]. Both increasing bilabellings naturally lead to hook-length formulas for trees and forests; in particular, one construction give...
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In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in the tree can get multiple labels. For all tree classes we show characterizations of suitable generating functions for the tree enumeration sequence via diff...
متن کاملOn Han's Hook Length Formulas for Trees
Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han’s formulas has been generalized to k-ary trees by Yang. Sagan has found a probabilistic proof of Yang’s extension. We give combinatorial proofs of Yang’s formula for k-ary trees and the other formula of Han for binary trees. Our bijections are based on the structure of k-ary trees ass...
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— We find two new hook length formulas for binary trees. The particularity of our formulas is that the hook length h v appears as an exponent. Consider the set B (n) of all binary trees with n vertices. It is well-known that the cardinality of B (n) is equal to the Catalan number (see, e.g., [9, p.220]): (1) T ∈B(n) 1 = 1 n + 1 2n n. For each vertex v of a binary tree T ∈ B (n) the hook length ...
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Recently Han obtained a general formula for the weight function corresponding to the expansion of a generating function in terms of hook lengths of binary trees. In this paper, we present formulas for k-ary trees, plane trees, plane forests, labeled trees and forests. We also find appropriate generating functions which lead to unifications of the hook length formulas due to Du and Liu, Han, Ges...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.09.043