Related papers: Forcing with Bushy Trees
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, 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…
Extending Mart\'in Escard\'o's effectful forcing technique, we give a new proof of a well-known result: Brouwer's monotone bar theorem holds for any bar that can be realized by a functional of type $(\mathbb{N} \to \mathbb{N}) \to…
Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this…
We show that it is consistent from an inaccessible cardinal that classical Namba forcing has the weak $\omega_1$-approximation property. In fact, this is the case if $\aleph_1$-preserving forcings do not add cofinal branches to…
Random forests are a type of ensemble method which makes predictions by combining the results of several independent trees. However, the theory of random forests has long been outpaced by their application. In this paper, we propose a novel…
We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string…
The main goal of this paper is to provide an algorithm for the random sampling of Butcher trees and the probabilistic numerical solution of ordinary differential equations (ODEs). This approach complements and simplifies a recent approach…
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and test them on a series of pedagogical…
We discuss the geometry of trees endowed with a causal structure using the conventional framework of equilibrium statistical mechanics. We show how this ensemble is related to popular growing network models. In particular we demonstrate…
In this paper we investigate the problem of the distributivity of Kurepa trees. We show that it is consistent that there are Kurepa trees and for every Kurepa tree there is a small forcing notion which adds a branch to it without collapsing…
We study the complexity and expressive power of conjunctive queries over unranked labeled trees represented using a variety of structure relations such as ``child'', ``descendant'', and ``following'' as well as unary relations for node…
We study some sequences of polynomials that appear when we consider the successive derivatives of the tree function (or Lambert's W function). We show in particular that they are related with a generalization of Cayley trees, called Greg…
In this paper, we focus on the prediction phase of a random forest and study the problem of representing a bag of decision trees using a smaller bag of decision trees, where we only consider binary decision problems on the binary domain and…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a…
To model discriminative, i.e. competition induced, self-thinning in even-aged forest stands a concept has been explored that discriminative mortality alters spatial arrangement of trees which in turn alters the mortality. Function of…
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…
This paper proposes the automatic Doubly Robust Random Forest (DRRF) algorithm for estimating the conditional expectation of a moment functional in the presence of high-dimensional nuisance functions. DRRF extends the automatic debiasing…