Related papers: Matroids that classify forests
We consider a random tree and introduce a metric in the space of trees to define the ``mean tree'' as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
This is a long introduction to the theory of "branch groups": groups acting on rooted trees which exhibit some self-similarity features in their lattice of subgroups.
We analyze the trade-off between model complexity and accuracy for random forests by breaking the trees up into individual classification rules and selecting a subset of them. We show experimentally that already a few rules are sufficient…
We prove that the class of trees with unique minimum edge-vertex dominating sets is equivalent to the class of trees with unique minimum paired dominating sets.
A premonoidal category is equipped only with a bifunctor and a natural isomorphism for associativity. We introduce a (deformation) natural automorphism representing the deviation from the Pentagon condition. We uncover a binary tree…
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher…
Stanley introduced the concept of chromatic symmetric functions of graphs which extends and refines the notion of chromatic polynomials of graphs, and asked whether trees are determined up to isomorphism by their chromatic symmetric…
We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…
We show that the fact that a political decision filtered through a finite tree of committees gives a determined answer generalises in some sense to infinite trees. This implies a new special case of the Matroid Intersection Conjecture.
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on $n$ vertices,…
Random Forests are one of the most popular classifiers in machine learning. The larger they are, the more precise is the outcome of their predictions. However, this comes at a cost: their running time for classification grows linearly with…
Arboreal categories were introduced as an axiomatic framework for game comonads, which provide a comonadic view on many model-comparison games in logic. We demonstrate the inadequacy of the axiom stating that paths are connected. We then…
The arithmetic of the natural numbers can be extended to arithmetic operations on planar binary trees. This gives rise to a non-commutative arithmetic theory. In this exposition, we describe this arithmetree, first defined by Loday, and…
We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings…
Meadows are a sort of commutative rings with a multiplicative identity element and a total multiplicative inverse operation. In this paper we study algebraic properties of common meadows, which are meadows that introduce, as the inverse of…
In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…
We present new and improved fixed-parameter algorithms for computing maximum agreement forests (MAFs) of pairs of rooted binary phylogenetic trees. The size of such a forest for two trees corresponds to their subtree prune-and-regraft…
We provide necessary and sufficient conditions on the unimodality of a convolution of two sequences of binomial coefficients preceded by a finite number of ones. These convolution sequences arise as as rank sequences of posets of…