Related papers: A One-to-One Correspondence between Natural Number…
We present a counter-example to the statement that there is a linear reduction in both directionsbetween the largest common subtree and the smallest common supertrees. Moreover, we show that in general, even having of one of them, it is…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting…
A combinatorial Gray code for a set of combinatorial objects is a sequence of all combinatorial objects in the set so that each object is derived from the preceding object by changing a small part. In this paper we design a Gray code for…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Knowledge representation and reasoning in law are essential to facilitate the automation of legal analysis and decision-making tasks. In this paper, we propose a new approach based on legal science, specifically legal taxonomy, for…
The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of…
It is shown that a group defined by forbidding all patterns of size s+1 that do not appear in a given self-similar group of tree automorphisms is the topological closure of a self-similar, countable, regular branch group, branching over its…
Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…
As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "ordered leaf attachment" (OLA) method for uniquely encoding a…
We present an algorithm, called the Offset Tree, for learning to make decisions in situations where the payoff of only one choice is observed, rather than all choices. The algorithm reduces this setting to binary classification, allowing…
We give a combinatorial characterization of nodal curves admitting a natural d-th Abel map to their Picard scheme, for any positive integer d. "Natural" here means compatible with and independent of specialization.
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
In this short note we discuss recent results on hook length formulas of trees unifying some earlier results, and explain hook length formulas naturally associated to families of increasingly labelled trees.
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
In this note we discuss trees similar to the Calkin-Wilf tree, a binary tree that enumerates all positive rational numbers in a simple way. The original construction of Calkin and Wilf is reformulated in a more algebraic language, and an…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
We present the classical Stern-Brocot tree and provide a new proof of the fact that every rational number between 0 and 1 appears in the tree. We then generalize theStern-Brocot tree to allow for arbitrary choice of starting terms, and…
We study varieties that contain unranked tree languages over all alphabets. Trees are labeled with symbols from two alphabets, an unranked operator alphabet and an alphabet used for leaves only. Syntactic algebras of unranked tree languages…