Related papers: On the combinatorics of tableaux -- Graphical repr…
We propose efficient algorithms for enumerating the notorious combinatorial structures of maximal planar graphs, called canonical orderings and Schnyder woods, and the related classical graph drawings by de Fraysseix, Pach, and Pollack…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the…
Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse…
In this paper, we show how various combinatorial algorithms of Young tableaux naturally arise from the WKB approximation of the connection matrix of quantum confluent hypergeometric equation, including the Robinson-Schensted algorithm, the…
In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R^2, with a bounding face defined by a polygonal…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
We prove that the well-known condition of being a balanced labeling can be characterized in terms of the sliding algorithm on tower diagrams. The characterization involves a generalization of authors' Rothification algorithm. Using the…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
We introduce an insertion algorithm on Kohnert's combinatorial model for Demazure characters, generalizing Robinson--Schensted--Knuth insertion on tableaux. Our new insertion yields an explicit, nonnegative formula expressing the product of…
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
We revisit a concept that has been central in some early stages of computer science, that of structured programming: a set of rules that an algorithm must follow in order to acquire a structure that is desirable in many aspects. While much…
We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…
Floorplans are commonly used to represent the layout of buildings. In computer aided-design (CAD) floorplans are usually represented in the form of hierarchical graph structures. Research works towards computational techniques that…
Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…
Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…