Related papers: The tree structure in staircase tableaux

Much of the information about the multi-valley structure of disordered spin systems can be convened in a simple tree structure -- a barrier tree -- the leaves and internal nodes of which represent, respectively, the local minima and the…

The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…

Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…

We propose a novel framework for analyzing the geometric structure of horseshoes arising in three- and four-dimensional H\'enon-type maps by introducing paperfolding structures as geometric templates. These structures capture the folding…

Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…

Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…

Staged trees are probabilistic graphical models capable of representing any class of non-symmetric independence via a coloring of its vertices. Several structural learning routines have been defined and implemented to learn staged trees…

Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…

The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex…

In this paper, we deal with analytic and geometric properties of orthogonally convex sets. We establish a Blaschke-type theorem for path-connected and orthogonally convex sets in the plane using orthogonally convex paths. The separation of…

Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…

Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle…

We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…

Network visualization allows a quick glance at how nodes (or actors) are connected by edges (or ties). A conventional network diagram of "contact tree" maps out a root and branches that represent the structure of nodes and edges, often…

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…

In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux…

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…

We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of all dependent sequent calculi, and exhibiting it as the category of algebras for a monad on a presheaf…

Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations…