相关论文: A classification of plane and planar 2-trees

Several hook summation formulae for binary trees have appeared recently in the literature. In this paper we present an analogous formula for unordered increasing trees of size r, which involves r parameters. The right-hand side can be…

Peca suggested in a recent paper on the arxiv to consider binary butterfly trees and their Horton-Strahler numbers. The trees are obtained by glueing two binary trees together in a special way; the results are again binary trees but with a…

The purpose of this paper is twofold. First we answer to a question asked by Steingrimsson and Williams about certain permutation tableaux: we construct a bijection between binary trees and the so-called Catalan tableaux. These tableaux are…

We prove a weighted generalization of the formula for the number of plane vertex-labeled trees.

It implicitly follows from the work of [Colbourn, El-Mallah: On two dual classes of planar graphs. Discrete Mathematics 80(1): 21-40 (1990)] that every planar partial 3-tree is a subgraph of a planar 3-tree. This fact has already enabled to…

We introduce the combinatorial notion of posetted trees and we use it in order to write an explicit expression of the Baker-Campbell-Hausdorff formula.

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

We introduce a new family of higher-rank graphs, whose construction was inspired by the graphical techniques of Lambek \cite{Lambek} and Johnstone \cite{Johnstone} used for monoid and category emedding results. We show that they are planar…

We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…

We give a geometric method for determining the cohomology groups and the product structure of a polyhedral product, under suitable freeness conditions or with coefficients taken in a field. This is done by considering first a special class…

We are interested in the quantitative analysis of the compaction ratio for two classical families of trees: recursive trees and plane binary increasing trees. These families are typical representatives of tree models with a small depth.…

The m-Tamari lattice of F. Bergeron is an analogue of the clasical Tamari order defined on objects counted by Fuss-Catalan numbers, such as m-Dyck paths or (m+1)-ary trees. On another hand, the Tamari order is related to the product in the…

Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…

The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex…

We denote a polygon as a connected component in Cayley tree of order 2 containing certain number of fix vertices. We found an exact formula for a polygon counting problem for two cases, in which, for the first case the polygon contain a…

We use the theory of \Gamma-species to enumerate k-gonal and polygonal 2-trees with respect to their vertices. We then extend this result to enumerate "succulents", a tree-like class of graphs which generalize cacti.

We obtain an explicit formula for the Poincare duality isomorphism H^{n-3}(Mbar(ell)) to Z/2 for the space of isometry classes of n-gons with specified side lengths, if ell is monogenic in the sense of Hausmann-Rodriguez. This has potential…

We present a bijection from planar reduced trees to planar rooted hypertrees, which extends Knuth's rotation correspondence between planar binary trees and planar rooted trees. The operadic counterpart of the new bijection is explained.…

A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our…