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What is Alternative Proof of Couples Problem about?

This document presents an alternative proof of the Touchard-Kaplansky formula for the problème des ménages (couples problem) that counts the number of ways n couples can sit around a circular table without anyone sitting next to their partner or someone of the same gender. The proof uses dominos to represent couples sitting together, avoids prioritizing one gender by fixing the positions of one letter type first, and applies the principle of inclusion-exclusion. This approach combines the simplicity of usin

Author

Γιώργος Κοντογεωργίου

Language

EN