Related papers: A Combinatorial Identity for Rooted Labeled Forest…

For a specific rooted labeled tree topology, a labeled history is a sequence of branchings that give rise to that labeled topology as it unfolds over time. Here, for $r$-furcating trees, we use a connection with Huffman trees from…

Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…

Arborified multiple zeta values are a generalization of multiple zeta values associated with rooted trees. There are two types of decorated rooted trees, corresponding respectively to the series and the integral expressions. Manchon…

A recent paper (Manceau and Lambert, 2016) developed a novel approach for describing two well-defined notions of 'species' based on a phylogenetic tree and a phenotypic partition. In this paper, we explore some further combinatorial…

Exploratory data analysis is crucial for developing and understanding classification models from high-dimensional datasets. We explore the utility of a new unsupervised tree ensemble called uncharted forest for visualizing class…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

We prove combinatorially some identities related to Euler's partition identity (the number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts). They were conjectured by Beck and proved by Andrews…

Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…

Recently, Andrews and EI Bachraoui discovered several companions for some famous $q$-series formulas, and derived some new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results…

We study mixed identities for oligomorphic automorphism groups of countable relational structures. Our main result gives sufficient conditions for such a group to not admit a mixed identity without particular constants. We study numerous…

This paper outlines a method to determine whether two label-regular directed trees, are isomorphic and when they are almost isomorphic. The approach involves reinterpreting label-regular directed trees as universal covers of rooted graphs.…

We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrew's in which he considers the generation function for partitions with respect to size, number of odd parts, and number of…

Han recently discovered new hook length identities for binary trees. In this paper, we extend Han's identities to binomial families of trees. Moreover, we present a bijective proof of one of the identities for the family of ordered trees.

We study a basis of the polynomial ring that we call forest polynomials. This family of polynomials is indexed by a combinatorial structure called indexed forests and permits several definitions, one of which involves flagged P-partitions.…

Richard P. Stanley conjectured that finite trees can be distinguished by their chromatic symmetric functions. In this paper, we prove an analogous statement for posets: Finite rooted trees can be distinguished by their order quasisymmetric…

A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…

Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word these maps induce linear relations between…

This paper studies how to use relation algebras, which are useful for high-level specification and verification, for proving the correctness of lower-level array-based implementations of algorithms. We give a simple relation-algebraic…

In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.

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…