Related papers: A disjoint union theorem for trees
We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of…
We prove a density version of the Halpern-L\"{a}uchli Theorem. This settles in the affirmative a conjecture of R. Laver. Specifically, let us say that a tree $T$ is homogeneous if $T$ has a unique root and there exists an integer $b\meg 2$…
For a labelled tree on the vertex set $[n]:=\{1,2,..., n\}$, define the direction of each edge $ij$ to be $i\to j$ if $i<j$. The indegree sequence of $T$ can be considered as a partition $\lambda \vdash n-1$. The enumeration of trees with a…
The longstanding conjecture of Halin characterizing the existence of normal spanning trees in infinite graphs has been recently proved by Max Pitz [3]. A critical step in the proof involves the construction of dominated torsos, whose…
Teminal Wiener index is one of the commonly used topological index in mathematical chemistry. If two or more chemical compounds have the same terminal Wiener index then they will have similar physico-chemical properties. In this work we…
Termination property of functions is an important issue in computability theory. In this paper, we show that repeated iterations of a function can induce an order amongst the elements of its domain set. Hasse diagram of the poset, thus…
The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…
Let \Gamma be a geometrically finite tree lattice. We prove a Khintchine-Sullivan type theorem for the Hausdorff measure of the points at infinity of the tree that are well approximated by the parabolic fixed points of G. Using Bruhat-Tits…
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…
We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.
We extend the theorem of Liouville on integration in finite terms to include dilogarithmic integrals. The results provide a necessary and sufficient condition for an element of the base field to have an antiderivative in a field extension…
The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these…
We provide a formulation of the univalence axiom in a universe category model of dependent type theory that is convenient to verify in homotopy-theoretic settings. We further develop a strengthening of the univalence axiom, called pointed…
We prove joint universality theorems on the half plane of absolute convergence for general classes of Dirichlet series with an Euler-product, where in addition to vertical shifts we also allow scaling. This generalizes our recent joint…
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 offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.
The theorem of factorisation forests shows the existence of nested factorisations -- a la Ramsey -- for finite words. This theorem has important applications in semigroup theory, and beyond. The purpose of this paper is to illustrate the…
We give a short elementary proof of Tutte and Nash-Williams' characterization of graphs with k edge-disjoint spanning trees.