Any pair of zero divisors fg=0 in the group ring Z[Σ_n] induces a partition of n-digit numbers into subsets U_e defined by linear inequalities on which the zero divisors act constantly, thereby defining a number trick.
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A symmetry approach to number tricks
Any pair of zero divisors fg=0 in the group ring Z[Σ_n] induces a partition of n-digit numbers into subsets U_e defined by linear inequalities on which the zero divisors act constantly, thereby defining a number trick.