Counting configurations - Colegiul National C. Negruzzi (Iași)

Article
Résumé de la production
A disc is divided into n sectors, each of which is to be painted with one of k possible colours, with the condition that two adjacent sectors have different colors. In a first part, two configurations which are obtained from each other by a rotation are considered as different, and the problem is solved firstly by a Python program for values of n, k up to n=12 and k=5. Then a general formula is obtained by means of a recurrence.
In a second part, the number of distinct configurations when we identify those that are obtained from each other by rotations is calculated for an example, but the general case remains open.
Mots clés
combinatoire
coloration
principe d'inclusion-exclusion
Python
Lecture conseillée
à partir du lycée