Related papers: The tree structure in staircase tableaux
Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking by special graphs. Signless formulas…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
We present a bijection between the set of standard Young tableaux of staircase minus rectangle shape, and the set of marked shifted standard Young tableaux of a certain shifted shape. Numerically, this result is due to DeWitt (2012).…
Merge trees are a type of topological descriptors that record the connectivity among the sublevel sets of scalar fields. They are among the most widely used topological tools in visualization. In this paper, we are interested in sketching a…
Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Vacillating tableaux are sequences of integer partitions that satisfy specific conditions. The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [Comm. Anal. Geom 14 (2006), 475-496; math.DG/0412169]. The definition of a tableau over a Lie algebra…
We study the complexity and expressive power of conjunctive queries over unranked labeled trees represented using a variety of structure relations such as ``child'', ``descendant'', and ``following'' as well as unary relations for node…
We discuss a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. We give several equivalent descriptions, and prove some algebraic and combinatorial properties. In addition, we characterize…
Tables are information-rich structured objects in document images. While significant work has been done in localizing tables as graphic objects in document images, only limited attempts exist on table structure recognition. Most existing…
We introduce and study suitable Poisson structures for four dimensional maps derived as lifts and specific periodic reductions of integrable lattice equations. These maps are Poisson with respect to these structures and the corresponding…
We give new interpretations of the $\nu$-Tamari lattice of Pr\'eville-Ratelle and Viennot. First, we describe it as a rotation lattice of $\nu$-trees, which uncovers the relation with known combinatorial objects such as tree-like tableaux…
We aim to give a pedagogic and essentially self-contained presentation of the construction of various stochastic objects appearing in the dynamical $\Phi^4_3$ model. The construction presented here is based on the use of paraproducts. The…
The task of this survey is to present various results on intersection patterns of convex sets. One of main tools for studying intersection patterns is a point of view via simplicial complexes. We recall the definitions of so called…
A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a…
To a definable subset of Z_p^n (or to a scheme of finite type over Z_p) one can associate a tree in a natural way. It is known that the corresponding Poincare series P(X) = \sum_i N_i X^i is rational, where N_i is the number of nodes of the…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…