Unbalanced Subtrees in Binary Rooted Ordered and Un-ordered Trees
نویسنده
چکیده
Binary rooted trees, both in the ordered and in the un-ordered case, are well studied structures in the field of combinatorics. The aim of this work is to study particular patterns in these classes of trees. We consider completely unbalanced subtrees, where unbalancing is measured according to the so-called Colless index. The size of the biggest unbalanced subtree becomes then a new parameter with respect to which we find several enumeration formulas.
منابع مشابه
Properties of Subtree-Prune-and-Regraft Operations on Totally-Ordered Phylogenetic Trees
We study some properties of subtree-prune-and-regraft (SPR) operations on leaflabelled rooted binary trees in which internal vertices are totally ordered. Since biological events occur with certain time ordering, sometimes such totally-ordered trees must be used to avoid possible contradictions in representing evolutionary histories of biological sequences. Compared to the case of plain leaf-la...
متن کاملCocommutative Hopf Algebras of Permutations and Trees
Consider the coradical filtration of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We show that the associated graded Hopf algebras are dual to the cocommutative Hopf algebras introduced in the late 1980’s by Grossman and Larson. These Hopf algebras are constructed from ordered trees and heap-ordered trees, respectively. We also sho...
متن کاملLR-Drawings of Ordered Rooted Binary Trees and Near-Linear Area Drawings of Outerplanar Graphs
We study a family of algorithms, introduced by Chan [SODA 1999], for drawing ordered rooted binary trees. Any algorithm in this family (which we name an LR-algorithm) takes in input an ordered rooted binary tree T with a root rT , and recursively constructs drawings ΓL of the left subtree L of rT and ΓR of the right subtree R of rT ; then either it applies the left rule, i.e., it places ΓL one ...
متن کاملA general bijective algorithm for trees.
Trees are combinatorial structures that arise naturally in diverse applications. They occur in branching decision structures, taxonomy, computer languages, combinatiorial optimization, parsing of sentences, and cluster expansions of statistical mechanics. Intuitively, a tree is a collection of branches connected at nodes. Formally, it can be defined as a connected graph without cycles. Schroder...
متن کاملMining Induced and Embedded Subtrees in Ordered, Unordered, and Partially-Ordered Trees
Many data mining problems can be represented with nonlinear data structures like trees. In this paper, we introduce a scalable algorithm to mine partially-ordered trees. Our algorithm, POTMiner, is able to identify both induced and embedded subtrees and, as special cases, it can handle both completely ordered and completely unordered trees (i.e. the particular situations existing algorithms add...
متن کامل