Related papers: An introduction to multiple gaps

This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…

This is a survey of results in the enumeration of lattice paths.

This is an introduction to type theory, synthetic topology, and homotopy type theory from a category-theoretic and topological point of view, written as a chapter for the book "New Spaces for Mathematics and Physics" (ed. Gabriel Catren and…

In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.

A brief overview is given of recent progress in understanding the dynamics of hot gauge theories.

Motivated by the Gilbreath conjecture, we develop the notion of the gap sequence induced by any sequence of numbers. We introduce the notion of the path and associated circuits induced by an originator and study the conjecture via the…

In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.

This is a long introduction to the theory of "branch groups": groups acting on rooted trees which exhibit some self-similarity features in their lattice of subgroups.

This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.

We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…

We give a survey of the analytic theory of matrix orthogonal polynomials.

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three…

This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…

This article is part introduction and part survey to the mathematical area centered around local cohomology.

In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…