Free public beta until December 4, 2026: every course is open, no card needed. After that, the first chapter of each course stays free and full access is a one-time $39 ($19 for up to 100 founding members chosen for helpful feedback). Your progress is kept. How the beta works

parity of a permutation

Whether a permutation decomposes into an even or an odd number of transpositions -- every decomposition of the same permutation shares one parity, so it's well-defined.

Loading interactive…

Examples

$(1\,2\,3)=(1\,3)(1\,2)$ is even (two transpositions); $(1\,2)$ alone is odd.