Related papers: Acyclic heaps of pieces, I
We study heaps of pieces for lattice paths, which give a combinatorial visualization of lattice paths. We introduce two types of heaps: type $I$ and type $II$. A heap of type $I$ is characterized by peaks of a lattice path. We have a…
The objective of this series is to study metric geometric properties of (coarse) disjoint unions of amenable Cayley graphs. We employ the Cayley topology and observe connections between large scale structure of metric spaces and group…
The correspondence between Lie algebras, Lie groups, and algebraic groups, on one side and commutative Hopf algebras on the other side are known for a long time by works of Hochschild-Mostow and others. We extend this correspondence by…
The deep interconnection between linear algebra and graph theory allows one to interpret classical matrix invariants through combinatorial structures. To each square matrix A over a commutative ring K, one can associate a weighted directed…
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These…
Heaps are para-associative ternary operations bijectively exemplified by groups via the operation $(x,y,z) \mapsto x y^{-1} z$. They are also ternary self-distributive, and have a diagrammatic interpretation in terms of framed links.…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
The partially asymmetric exclusion process (PASEP) 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. It is partially…
The paper analyses the convergence of the $p$-version of the FEM when the solution is piecewise analytic function. It focuses on pointwise convergence of the gradient. It shows that at boundary the rate is different than inside the element…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
The adjunction between coalgebras and Hopf algebras, first described by Takeuchi, allows one to prove that the semi-abelian category of cocommutative Hopf algebras has enough $\mathcal E$-projective objects with respect to the class…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We introduce two new algebras that we call \emph{tied--boxed Hecke algebra} and \emph{tied--boxed Temperley--Lieb algebra}. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second…
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the…
We study the Manneville map f(x)=x+x^z (mod 1), with z>1, from a computational point of view, studying the behaviour of the Algorithmic Information Content. In particular, we consider a family of piecewise linear maps that gives examples of…
Using the shuffle structure of the graphs, we introduce a new kind of the Hopf algebraic structure for tagged graphs with, or without loops. Like a quantum group structure, its product is non-commutative. With the help of the Hopf algebraic…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
Determining the material properties of layered systems like graphite and bigraphene from \emph{ab initio} calculations is very difficult. This is mostly due to the complex van der Waals forces which help bind the layers. Recently,…
In prior joint work with Lewis, we developed a theory of enriched set-valued $P$-partitions to construct a $K$-theoretic generalization of the Hopf algebra of peak quasisymmetric functions. Here, we situate this object in a diagram of six…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…