Related papers: A disjoint union theorem for trees

We prove an explicit formula for the tail of the colored Jones polynomial for a class of arborescent links in terms of a product of theta functions and/or false theta functions. We also provide numerical evidence towards a classification of…

We show the density theorem for the class of finite oriented trees ordered by the homomorphism order. We also show that every interval of oriented trees, in addition to be dense, is in fact universal. We end by considering the fractal…

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. In this paper we will show that those combined extensions can be made if we…

We extend Tilson's theory of the algebra of finite categories, in particular, the Derived Category Theorem, to the setting of forest algebras. As an illustration of the usefulness of this method, we provide a new proof of a result of Place…

We prove a weighted generalization of the formula for the number of plane vertex-labeled trees.

Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…

We give a formula for the relative Deligne tensor product of two indecomposable finite semisimple module categories over a pointed braided fusion category over an algebraically closed field.

In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the establishment of a resolvent identity, which serves as an…

Several hook summation formulae for binary trees have appeared recently in the literature. In this paper we present an analogous formula for unordered increasing trees of size r, which involves r parameters. The right-hand side can be…

We present in this paper a first-order axiomatization of an extended theory $T$ of finite or infinite trees, built on a signature containing an infinite set of function symbols and a relation $\fini(t)$ which enables to distinguish between…

We define a bivariate polynomial for unlabeled rooted trees and show that the polynomial of an unlabeled rooted tree $T$ is the generating function of a class of subtrees of $T$. We prove that the polynomial is a complete isomorphism…

We provide new and purely combinatorial proofs of two infinite extensions of the Hales--Jewett theorem. The first one is due to T. Carlson and S. Simpson and the second one is due T. Carlson. Both concern infinite increasing sequences of…

We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…

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…

We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a {\em tree algebra}. Using the Riemann-Hilbert correspondence, we…

We prove a fix point theorem for monoids of self-embeddings of trees. As a corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either contains a subdivided binary tree as a subtree or has a vertex, and edge, an end or…

Generalizing a well known theorem for finite matroids, we prove that for every (infinite) connected matroid M there is a unique tree T such that the nodes of T correspond to minors of M that are either 3-connected or circuits or cocircuits,…

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…