Log-Concavity of Littlewood-Richardson Coefficients via Symmetric Functions — E8 Intelligence Research

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Littlewood-Richardson coefficients are log-concave, and their refinements and saturation properties can be characterized using symmetric function theory and lattice/root-system frameworks. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22245193

September 2, 2026Open Access

Log-Concavity of Littlewood-Richardson Coefficients via Symmetric Functions — E8 Intelligence Research

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Key Points

To investigate the log-concavity, saturation properties, and structural deformations of Littlewood-Richardson coefficients using symmetric function theory and root lattice frameworks.
Analyzed Littlewood-Richardson coefficients formulated as Schur polynomial inner products within symmetric function theory.
Mapped coefficient progressions onto partition dominance orders organized as type A root lattices.
Examined saturation behavior and refinements under flagged and quantum deformations.
Established log-concavity along the dominance order, satisfying the relation (c_ν)^2 ≥ c_{ν-α} c_{ν+α}.
Demonstrated saturation consistency where positive coefficients remain strictly positive under integer scaling (c_{λ,μ}^{ν} > 0 iff c_{Nλ,Nμ}^{Nν} > 0).

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Implication

Theoretical analysis demonstrates log-concavity in Littlewood-Richardson coefficient sequences along the dominance order, indicating structural lattice bounds in algebraic geometry.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9a862b5d9e33f25c631d14 https://doi.org/10.5281/zenodo.22245193

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Log-Concavity of Littlewood-Richardson Coefficients via Symmetric Functions — E8 Intelligence Research

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Log-Concavity of Littlewood-Richardson Coefficients via Symmetric Functions — E8 Intelligence Research

Key Points

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Implication

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