The Aperiodical 

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Stirling’s numbers in a nutshell

By Audace Amen Vioutou Dossou-Olory. Posted October 25, 2017

This is a guest post by researcher Audace Dossou-Olory of Stellenbosch University, South Africa.

In assignment problems, one wants to find an optimal and efficient way to assign objects of a given set to objects of another given set. An assignment can be regarded as a bijective map $\pi$ between two finite sets $E$ and $F$ of $n\ge 1$ elements. By identifying the sets $E$ and $F$ with $\{1,2,\dots ,n\}$, we can represent an assignment by a permutation.

Circular reasoning on Catalan numbers

By Audace Amen Vioutou Dossou-Olory. Posted October 16, 2017

This is a guest post by researcher Audace Dossou-Olory of Stellenbosch University, South Africa.

Consider the following question: How many ways are there to connect $2n$ points on a circle so that each point is connected to exactly one other point?