Related papers: From factorizations of noncommutative polynomials …

This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…

A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…

This is an exposition of some recent developments related to the object in the title, particularly the combinatorial computation of the (genus 0) Gromov-Witten invariants of the flag manifold and the quadratic algebra approach. The notes…

These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…

This is an expanded version of the notes of my three lectures at a NATO Advanced Study Institute ``Symmetric functions 2001: surveys of developments and perspectives" (Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; June…

Recent developments have found unexpected connections between non-commutative probability theory and algebraic topology. In particular, Boolean cumulants functionals seem to be important for describing morphisms of homotopy operadic…

This expository essay is aimed at introducing the Jones polynomial. We will see the encapsulation of the Jones polynomial, which will involve topics in functional analysis and geometrical topology; making this essay an interdisciplinary…

Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…

This is an expanded version of the notes for the lectures given by the author at RIMS in the summer of 1999 to give a detailed account of the proof for the (weak) factorization theorem of birational maps by…

This paper describes in detail how (discrete) quaternions - ie. the abstract structure of 3-D space - emerge from, first, the Void, and thence from primitive combinatorial structures, using only the exclusion and co-occurrence of otherwise…

This is an expanded version of the talk I gave at Oberwolfach, MIT and several other universities.

In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in…

This is a chapter in an incoming book on aperiodic order. We review results about the topology, the dynamics, and the combinatorics of aperiodically ordered tilings obtained with the tools of noncommutative geometry.

In the multicentric calculus one takes a polynomial with simple roots as a new global variable and replaces scalar functions {\varphi} by functions f taking values in C^d with d the degree of the polynomial leading to an efficient…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…

This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical…

We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…

This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…

Bell polynomials appear in several combinatorial constructions throughout mathematics. Perhaps most naturally in the combinatorics of set partitions, but also when studying compositions of diffeomorphisms on vector spaces and manifolds, and…