Related papers: Dyck tableaux
In the aim to understand the generalization of Stirling numbers occurring in the bosonic normal ordering problem, several combinatorial models have been proposed. In particular, Blasiak \emph{et al.} defined combinatorial objects allowing…
We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
Hypermaps were introduced as an algebraic tool for the representation of embeddings of graphs on an orientable surface. Recently a bijection was given between hypermaps and indecomposable permutations; this sheds new light on the subject by…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
We introduce a new class of numerical schemes which allow for low regularity approximations to the expectation $ \mathbb{E}(|u_{k}(\tau, v^{\eta})|^2)$, where $u_k$ denotes the $k$-th Fourier coefficient of the solution $u$ of the…
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…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
A circular Pascal array is a periodization of the familiar Pascal's triangle. Using simple operators defined on periodic sequences, we find a direct relationship between the ranges of the circular Pascal arrays and numbers of certain…
Introduced in the late 1960's, the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with…
Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class,…
We extend the notion of mex, which is central in combinatorial number theory, to an arbitrary combinatorial structure, and we prove a general theorem to determine the generating function of the objects having fixed mex. We then study this…
Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…
Proposing new materials by atom substitution based on periodic table similarity is a conventional strategy of searching for materials with desired property. We introduce a machine learning frame work that promotes this paradigm to be…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well…
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer…