SWhat changed
For a finite permutation group acting on s positions and an inventory series f with finite nonnegative integer coefficients, the generating series of inequivalent configurations is obtained by replacing each cycle-index variable z_j with f(x^j,y^j,...). Fixed colour multiplicities are extracted coefficientwise; the proof counts cycle-constant fixed configurations and averages over the group.
Scientific scope
For a finite permutation group acting on s positions and an inventory series f with finite nonnegative integer coefficients, the generating series of inequivalent configurations is obtained by replacing each cycle-index variable z_j with f(x^j,y^j,...). Fixed colour multiplicities are extracted coefficientwise; the proof counts cycle-constant fixed configurations and averages over the group. Finite permutation action and coefficientwise finite inventories; the series is formal and analytic convergence is not assumed. This record covers the cycle-index theorem, not every tree asymptotic or molecular example in the 110-page paper. Orbit-stabilizer/fixed-point averaging is inherited background. No exclusive priority over Redfield’s 1927 work is claimed.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Finite permutation action and coefficientwise finite inventories; the series is formal and analytic convergence is not assumed. This record covers the cycle-index theorem, not every tree asymptotic or molecular example in the 110-page paper. Orbit-stabilizer/fixed-point averaging is inherited background. No exclusive priority over Redfield’s 1927 work is claimed.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
Full scientific record · Browse contribution grades · Request a correction