Catalan numbers
Maths circle meeting on 21 January 2026 (18-21 h)
Room and time: virtual/online with the video conferencing software Zoom (Paderborn University campus licence) from 18:00 to 21:00 (on Wed. 21.01.2026) 10:00 to 13:00 (on Sat. 24.01.2026)
Leader of the workshop: Dr Kerstin Hesse
Description: In how many different ways can a plane convex n-square be decomposed into triangles by connecting vertices? Decompositions that merge into each other by rotation or reflection are considered to be different. (A triangle has only one decomposition, and a quadrilateral can be decomposed in two ways with a diagonal into two triangles each. A pentagon has five decompositions into three triangles each. After that it gets more complicated). The answer to this question leads us to the sequence of Catalan numbers: 1, 2, 5, 14, 42, 132, .... Surprisingly, Catalan numbers occur in many other problems, e.g. in decision trees or in certain minimal grid paths in a rectangular road network or in a problem with forward and backward steps. - We learn about five different problems in which Catalan numbers occur, and in the additional exercises we also prove that these problems are all equivalent. Using these different but equivalent problems, we will then work together to prove the formula for calculating Catalan numbers.
Website with registration form: math.uni-paderborn.de/mathezirkel/
