Related papers: Assigned rational functions of a rooted tree

A symbolic-computational algorithm, fully implemented in Maple, is described, that computes explicit expressions for generating functions that enable the efficient computations of the expectation, variance, and higher moments, of the random…

In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical meromorphic functions, emphasizing practical techniques that can really carry out computations. For…

For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…

We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of…

We investigate the spectral properties of balanced trees and dendrimers, with a view toward unifying and improving the existing results. Here we find a semi-factorized formula for their characteristic polynomials. Afterwards, we determine…

In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and…

We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…

The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from…

Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…

In this paper we study the adjacency spectrum of families of finite rooted trees with regular branching properties. In particular, we show that in the case of constant branching, the eigenvalues are realized as the roots of a family of…

We explore the relationship between polynomial functors and (rooted) trees. In the first part we use polynomial functors to derive a new convenient formalism for trees, and obtain a natural and conceptual construction of the category…

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…

We define a ring whose elements are rational functions, whose addition is polynomial multiplication, and whose multiplication is a convolution operation. It is then show that this ring's endomorphisms exhibit a strong classification.…

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…

We construct rational all-pass matrix functions with real-valued coefficients for mirroring pairs of complex-conjugated determinantal roots of a rational matrix. This problem appears, for example, when proving the spectral factorization…

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

The perturbation expansion of the solution of a fixed point equation or of an ordinary differential equation may be expressed as a power series in the perturbation parameter. The terms in this series are indexed by rooted trees and depend…

The purpose of the paper is to present quantitative estimates for the principal eigenvalue of discrete p-Laplacian on the set of rooted trees. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequality. Three…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and…