A cyclic-orbit decomposition of the Leibniz formula yields sign laws, a rectification theorem, and a proof that no fixed-width Sarrus-style rule exists for n greater than or equal to 4.
Enumerative Combinatorics, Volume 1 (2nd ed.)
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ARE Method: Orbital Decompositions and Dihedral Cancellations for Determinants
A cyclic-orbit decomposition of the Leibniz formula yields sign laws, a rectification theorem, and a proof that no fixed-width Sarrus-style rule exists for n greater than or equal to 4.