What does cycle and $M=M_c$ mean?
2026-04-13 05:03:46.1776056626
Determine the permutation matrix of a permutation in $S_{n}$
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A cycle (or a cyclic permutation) $c$ is a specific kind of permutation where each element is moved one place to the side, and then the element at the end is moved to the beginning. $M_c$ is the corresponding permutation matrix. It has $1$ in all entries just below the main diagonal, a $1$ in the top right corner, and otherwise $0$ everywhere (assuming that $c$ permutes all the elements of our set)