Related papers: About Fibonacci trees. I
We prove that an irreducible lattice acting on a product of two or more locally finite, biregular trees is finitely generated.
It was shown in \cite{sc12} that for a certain class of structures $\I$, $\I$-indexed indiscernible sets have the modeling property just in case the age of $\I$ is a Ramsey class. We expand this known class of structures from ordered…
We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numerical semigroups, we analyze some of its properties and use…
To the known fact that Parsimony method sometimes fails on the problem of inferring species trees from gene trees, here we proved that no mater of what topology the true 9-taxon and greater species tree is the only thing one needs to break…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M in C as long as possible, we get a root of M. Our main result is that under certain conditions the root of any object exists…
Determining whether two graphs are isomorphic is an important and difficult problem in graph theory. One way to make progress towards this problem is by finding and studying graph invariants that distinguish large classes of graphs. Stanley…
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
This paper, dating from May 1991, contains preliminary (and unpublishable) notes on investigations about iteration trees. They will be of interest only to the specialist. In the first two sections I define notions of support and embeddings…
By weighted tree we understand such connected tree,that: a) each its vertex and each edge have a positive integer weight; b) the weight of each vertex is equal to the sum of weights of outgoing edges. Each tree has a binary structure --- we…
We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…
An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…
It is shown that shape preservation is decidable for top-down tree transducers, bottom-up tree transducers, and for compositions of total deterministic macro tree transducers. Moreover, if a transducer is shape preserving, then it can be…
We present an alternate proof of the passage from the finiteness principle for metric trees to the construction of the core in the C. Fefferman and Shvartsman finiteness theorem for Lipschitz selection problems.
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet…
A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…