Sentence examples for planar tree from inspiring English sources

The reduced planar tree formula is proved by recursion, and again by an unusual cancellation technique.

The order of the factors in each summand is determined by the breadth first ordering on the vertices of the planar tree.

RAG represents RNA 2D structure as planar tree or dual graphs to assist the cataloging, analyzing, and designing of RNA structures.

Call a planar tree with n leaves decorated whenever the leaves are labeled by [ n ] = { 1, 2, 3, …, n } for n ∈ N and every vertex is labeled by an element of V.

By contrast, the non-commuting monomials of SH are labeled by colored planar trees.

Finally there is a parallel to Haiman and Schmitt's reduced tree formula for the antipode, in which one uses reduced planar trees and the depth first ordering on the vertices.

We express the elements of the free shuffle operad using planar trees.

These planar trees are substantially easier to analyze: for example, there is a nice closed form generating function for the numbers of such trees (the Catalan numbers).

Steyaert and Flajolet [ 22] investigate the occurrences of subtrees in the case of "planar" trees, i.e. trees that are equipped with an order of subtrees at every internal node.

Each ascending axon terminates at a specific depth of the molecular layer according to the timing of GC differentiation and bifurcates into a parallel fiber that runs parallel to the pial surface and intersects perpendicularly the planar dendritic trees of numerous Purkinje cells, which are the major postsynaptic partners of GCs (Figure 4A) [43], [44], [45], [45].

There currently exists a plethora of layout algorithms for particular classes of graphs, such as trees, planar graphs or DAGs, for which effective solutions have been found that give good results, not only in terms of time/space complexity but also in terms of aesthetic criteria.