相关论文: Tree-like properties of cycle factorizations

We consider the mutation--selection differential equation with pairwise interaction (or, equivalently, the diploid mutation--selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the…

We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…

In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed…

The Matrix-Tree Theorem states that the number of spanning trees of a graph is given by the absolute value of any cofactor of the Laplacian matrix of the graph. We propose a very short proof of this result which amounts to comparing Taylor…

We extend classical results on simple varieties of trees (asymptotic enumeration, average behavior of tree parameters) to trees counted by their number of leaves. Motivated by genome comparison of related species, we then apply these…

We consider Hilbert series associated to modules over various categories of trees. Using the technology of Sam and Snowden, we show that these Hilbert series must be algebraic. We then apply these technical theorems to prove facts about…

The displayed tree phylogenetic network model is shown to sit as a natural submodel of the graphical model associated to a directed acyclic graph (DAG). This representation allows to derive a number of results about the displayed tree…

A semiorder is a partially ordered set $P$ with two certain forbidden induced subposets. This paper establishes a bijection between $n$-element semiorders of length $H$ and $(n+1)$-node ordered trees of height $H+1$. This bijection…

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation…

The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that…

We show that certain digraphs with the same vertex set but different arc sets have the same sum over the weights of all arborescences with a given root vertex. We relate our results to the Matrix-Tree Theorem and show how they provide a…

We consider the problem of enumerating d-irreducible maps, i.e. planar maps whose all cycles have length at least d, and such that any cycle of length d is the boundary of a face of degree d. We develop two approaches in parallel: the…

Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…

Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…

We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a complexity of natural number $n$ is…

The number of spanning trees in a class of directed circulant graphs with generators depending linearly on the number of vertices $\beta n$, and in the $n$-th and $(n-1)$-th power graphs of the $\beta n$-cycle are evaluated as a product of…

It was recently observed by de Vienne et al. that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on…

We present a nice result on the probability of a cycle occurring in a randomly generated graph. We then provide some extensions and applications, including the proof of the famous Cayley formula, which states that the number of labeled…

In 1989 Erd\H{o}s and Sz\'ekely showed that there is a bijection between (i) the set of rooted trees with $n+1$ vertices whose leaves are bijectively labeled with the elements of $[\ell]=\{1,2,\dots,\ell\}$ for some $\ell \leq n$, and (ii)…

This work addresses an enumeration problem on weighted bi-colored plane trees with prescribed vertex data, with all vertices labeled distinctly. We give a bijection proof of the enumeration formula originally due to Kochetkov, hence…