Related papers: Binary trees using the bookshelf and baseball cons…
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
Bargraphs are a special class of convex polyominoes. They can be identified with lattice paths with unit steps north, east, and south that start at the origin, end on the $x$-axis, and stay strictly above the $x$-axis everywhere except at…
We introduce a monoid structure on a certain set of labelled binary trees, by a process similar to the construction of the plactic monoid. This leads to a new interpretation of the algebra of planar binary trees of Loday-Ronco.
We establish counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form $x\_i-x\_j=s$ for some integer $s$. Classical…
In this work, the partially and totally hom-coassociative ternary coalgebras are constructed and discussed. Their {infinitesimal} bialgebraic structures are also investigated. The related dual space structures and their properties are…
This paper introduces a series of methods for traversing binary decision trees using arithmetic operations. We present a suite of binary tree traversal algorithms that leverage novel representation matrices to flatten the full binary tree…
We present new links between some remarkable martingales found in the study of the Binary Search Tree, or of the Bisection Problem, looking at them on the probability space of a continuous time binary branching process.
In this paper, we provide new insights and analysis for the two elementary tree-based data structures - the AVL tree and binary heap. We presented two simple properties that gives a more direct way of relating the size of an AVL tree and…
Tree-like tableaux are combinatorial objects that appear in a combinatorial understanding of the PASEP model from statistical mechanics. In this understanding, the corners of the Southeast border correspond to the locations where a particle…
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…
Islands are combinatorial objects that can be intuitively defined on a board consisting of a finite number of cells. Based on the neighbor relation of the cells, it is a fundamental property that two islands are either containing or…
We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type B, we show the existence of basic sets for the matrices of constructible representations. Then we study…
We show new bijective proofs of previously known formulas for the number of regions of some deformations of the braid arrangement, by means of a bijection between the no-broken-circuit sets of the corresponding integral gain graphs and some…
We investigate finite right-distributive binary algebraic structures called shelves. We first use symbolic computations with Python to classify (up to isomorphism) all connected shelves with order less than six. We explore the group…
Binary multirelations form a model of alternating nondeterminism useful for analysing games, interactions of computing systems with their environments or abstract interpretations of probabilistic programs. We investigate this alternating…
In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an…
We give a descriptive construction of trees for multi-ended graphs, which yields yet another proof of Stallings' theorem on ends of groups. Even though our proof is, in principle, not very different from already existing proofs and it draws…
A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced with the aim of giving a common language to most of the structures…
The goal of this brief pedagogical article is to show that Binary Decision Diagrams are a special kind of Bayesian Net. This observation is obvious to workers in these two fields, but it might not be too obvious to others.
We interpret noncrossing partitions of type $B$ and type $D$ in terms of noncrossing partitions of type $A$. As an application, we get type-preserving bijections between noncrossing and nonnesting partitions of type $B$, type $C$ and type…