Related papers: Tiered trees and Theta operators

We discuss some applications of fusion rules and intertwining operators in the representation theory of cyclic orbifolds of the triplet vertex operator algebra. We prove that the classification of irreducible modules for the orbifold vertex…

This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a subset of the tree-like tableaux previously defined by…

Inspired by [Qiu, Wilson 2019] and [D'Adderio, Iraci, Vanden Wyngaerd 2019 - Delta Square], we formulate a generalised Delta square conjecture (valley version). Furthermore, we use similar techniques as in [Haglund, Sergel 2019] to obtain a…

Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…

This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The…

Inspired by natural classes of examples, we define generalized directed semi-tree and construct weighted shifts on the generalized directed semi-trees. Given an $n$-tuple of directed directed semi-trees with certain properties, we associate…

If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $\lambda \mapsto \delta \left(\lambda I-T\right) $ at…

We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…

An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any…

Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…

In this paper, we define and study the arithmetic of the ring of $\mathbb{U}$-operators for reductive $p$-adic groups. These operators generalise the notion of "successor" operators for trees with a marked end. We show that they are…

We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables…

In their work on `Coxeter-like complexes', Babson and Reiner introduced a simplicial complex $\Delta_T$ associated to each tree $T$ on $n$ nodes, generalizing chessboard complexes and type A Coxeter complexes. They conjectured that…

We introduce the notion of (Ramsey) action of a tree on a (filtered) semigroup. We then prove in this setting a general result providing a common generalization of the infinitary Gowers Ramsey theorem for multiple tetris operations, the…

In this paper we continue the study of codes over imaginary quadratic fields and their weight enumerators and theta functions. We present new examples of non-equivalent codes over rings of characteristic $p=2$ and $p=5$ which have the same…

We determine the special values at positive integers of the spectral zeta function associated with the combinatorial Laplacian on the regular tree. These values admit explicit formulas in terms of certain polynomials, which we show to be…

A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and…

We take advantage of the combinatorial interpretations of many sequences of polynomials of binomial type to define a sequence of symmetric functions corresponding to each sequence of polynomials of binomial type. We derive many of the…

Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains…

We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in "An operad of non-commutative independences defined by trees" (Dissertationes Mathematicae, 2020, doi:10.4064/dm797-6-2020),…