Related papers: De combinatoriek van De Bruijn
Motivated by a polynomial identity of certain iterated integrals, first observed in [CGM20] in the setting of lattice paths, we prove an intriguing combinatorial identity in the shuffle algebra. It has a close connection to de Bruijn's…
This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of…
This is an English translation of Reidemeister's book "Einf\"uhrung in die kombinatorische Topologie" from 1932, the first monograph on combinatorial group theory and topology, with some added comments by the translator and Warren Dicks.
We present an explicit combinatorial realization of the commutor in the category of crystals which was first studied by Henriques and Kamnitzer. Our realization is based on certain local moves defined by van Leeuwen.
In the article "Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane" we constructed the continuous hull for the combinatorics of "A regular pentagonal tiling of the plane", and in the…
We propose a new algorithm for merging succinct representations of de Bruijn graphs introduced in [Bowe et al. WABI 2012]. Our algorithm is based on the lightweight BWT merging approach by Holt and McMillan [Bionformatics 2014, ACM-BCB…
We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition…
We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…
In literature, many important combinatorial properties of subsets of N have been studied both with nonstandard techniques and from the point of view of N. In this thesis we mix these two different approaches in a technique that, at the same…
This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
Binary data are highly common in many applications, however it is usually modelled with the assumption that the data are independently and identically distributed. This is typically not the case in many real-world examples and such the…
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
We study variants of the well-known Collatz graph, by considering the action of the 3n+1 function on congruence classes. For moduli equal to powers of 2, these graphs are shown to be isomorphic to binary De Bruijn graphs. Unlike the Collatz…
In a previous paper (arXiv:1410.5207) certain birational transformations were constructed between the noncommutative schemes associated to quadratic and cubic three dimensional Sklyanin algebras. In the current paper we consider the inverse…
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
A recursive scheme relying on decagons is used to generate Penrose-like sublattices or tilings. Its relevance for understanding structures with non-crystallographic symmetry is discussed.