Related papers: Trees meet octahedron comparison
We prove that the wreath product orbifolds studied earlier by the first author provide a large class of higher dimensional examples of orbifolds whose orbifold Hodge numbers coincide with the ordinary ones of suitable resolutions of…
We construct measures invariant with respect to equivalence relations which are graphed by horospheric products of trees. The construction is based on using conformal systems of boundary measures on treed equivalence relations. The…
We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the…
We give a short and elementary proof of the fact that every metric space of finite asymptotic dimension can be embedded into a finite product of trees.
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.
Trees can be regarded as discrete analogue of Hadamard manifolds, namely simply-connected Riemannian manifolds of non-positive sectional curvature. In this paper, we compare the first (non-trivial) Steklov eigenvalue and algebraic…
Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.
We investigate the matched product of solutions associated with right and left shelves. First, we prove that the requirements to provide the matched product of solutions that come from shelves can be simplified. Then we give conditions for…
In this paper we determine the parity of some sequences which are related to Catalan numbers. Also we introduce a combinatorical object called, \Catalan tree", and discuss its properties.
We show that for the edge ideals of a certain class of forests, the arithmetical rank equals the projective dimension.
Ancestral mixture model, proposed by Chen and Lindsay (2006), is an important model to build a hierarchical tree from high dimensional binary sequences. Mixture trees created from ancestral mixture models involve in the inferred…
We prove an infinitary disjoint union theorem for level products of trees. To implement the proof we develop a Hales-Jewett type result for words indexed by a level product of trees.
We extend decision tree and random forest algorithms to product space manifolds: Cartesian products of Euclidean, hyperspherical, and hyperbolic manifolds. Such spaces have extremely expressive geometries capable of representing many…
We compute dimensions of graded components for free algebras with two compatible associative products, and give a combinatorial interpretation of these algebras in terms of planar rooted trees.
We start with an ``algebraic'' RSK-correspondence due to Noumi and Yamada. Given a matrix $X$, we consider a pyramidal array of solid minors of $X$. It turns out that this array satisfies an algebraic variant of octahedron recurrence. The…
In the present paper, we construct an invariant of braids in the real projective plane which corresponds to an ``action'' of braids on certain graphs in $\R{}P^{2}$ with labels. This paper is a sequel of papers \cite{M},\cite{KM}. It…
We show that there exists a quasi-isometric embedding of the product of $n$ copies of $\mathbb{H}_{\mathbb{R}}^2$ into any symmetric space of non-compact type of rank $n$, and there exists a bi-Lipschitz embedding of the product of $n$…
We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in [4]. We also establish maximal trees for the difference of average eccentricity and remoteness and…
Assume we are given a set of items from a general metric space, but we neither have access to the representation of the data nor to the distances between data points. Instead, suppose that we can actively choose a triplet of items (A,B,C)…
In this paper, we introduce the notion of Cartesian Forest, which generalizes Cartesian Trees, in order to deal with partially ordered sequences. We show that algorithms that solve both exact and approximate Cartesian Tree Matching can be…