Discrete Mathematics and Foundations

mathemathical subject image: 

Random sampling of domino and lozenge tilings

Submitted by IMAGINARY on

A grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by ar- ranging the cells in pairs. In this snapshot we review different strategies to generate random tilings of large grid regions in the plane. This makes it possible to observe the behaviour of large random tilings, in par- ticular the occurrence of boundary phenomena that have been the subject of intensive recent research. 

Domino tilings of the Aztec Diamond

Submitted by IMAGINARY on

Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with dominoes?

One specific paper cutout can be mathematically described as the so-called Aztec Diamond, and a way to cover it with dominoes is a domino tiling.

Wie man einen Sieger wählt: die Mathematik der Sozialwahl

Submitted by IMAGINARY on

Angenommen, eine Gruppe von Einzelpersonen möch- te unter verschiedenen Optionen wählen, zum Bei- spiel einen von mehreren Kandidaten für ein poli- tisches Amt oder den besten Teilnehmer einer Eis- kunstlaufmeisterschaft. Man könnte fragen: Was ist die beste Methode, einen Sieger in dem Sinne zu wäh- len, dass er die individuellen Präferenzen der Grup- penmitglieder am besten widerspiegelt?

Friezes and tilings

Submitted by IMAGINARY on

Friezes have occured as architectural ornaments for many centuries. In this snapshot, we consider the mathematical analogue of friezes as introduced in the 1970s by Conway and Coxeter. Recently, infinite versions of such friezes have appeared in current research. We are going to describe them and explain how they can be classified using some nice geometric pictures.

School Taskbook: From 5 to 15

Submitted by IMAGINARY on

The taskbook for school students by renowned Russian mathematician Prof. Vladimir Igorevich Arnold. You can find the original Russian version as well as an English, German, Spanish, Italian, Vietnamese and Turkish translation.

If you are interested to add a new translation, please see the github repository of the booklet for all sources and details.

Seiten