Sharp Higher-Chain Amplification Under a Single Cover Edit in Finite Posets

Q: What does this research mean for the field?

The maximum increase in the number of k-element chains when adding a single cover to a finite bounded poset of size n is exactly determined by a sharp extremal formula. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Panasenko

doi:10.5281/zenodo.22081814

August 24, 2026Open Access

Sharp Higher-Chain Amplification Under a Single Cover Edit in Finite Posets

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Key Points

To determine the exact maximum increase in the number of k-element chains within a finite bounded poset resulting from the addition of a single canonical Hasse cover.
Derived an exact local decomposition of chain changes across the newly introduced comparability bridge using lower- and upper-chain profiles.
Integrated the decomposition identity with a cover-preserving witness budget to evaluate extremal poset configurations.
Established a sharp extremal formula showing max ΔC_k = binom(n−2,k) − binom(floor((n−4)/2)+2,k) − binom(ceil((n−4)/2)+2,k) for all n ≥ 6 and k ≥ 3.
Demonstrated that chain creation is fundamentally constrained by the local decomposition across the new cover relation.

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Implication

Mathematical analysis demonstrates an exact upper bound for chain amplification in finite bounded posets, establishing the maximal structural impact of adding a single cover.

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Cite This Study

Panasenko (2026) studied this question.

synapsesocial.com/papers/6a8e9b68451774b83f3b4289 https://doi.org/10.5281/zenodo.22081814

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Sharp Higher-Chain Amplification Under a Single Cover Edit in Finite Posets

Key Points

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Implication

Discussion

Cite This Study

Sharp Higher-Chain Amplification Under a Single Cover Edit in Finite Posets

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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