Local comparison counting for linear extensions and a bounded-range balance refinement
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Abstract
For uniform linear extensions of finite posets with bounded maximum incomparability degree, a local stable-partition estimate tracks the incomparability budget consumed by conditioning. The resulting three-vertex order bound gives a sharper explicit bounded-range balance estimate through the established finite-boundary argument. A complementary two-chain construction quantifies a rare-triple obstruction to reusing the sharp pair denominator. Complete proofs and exact finite reproducibility code accompany these counting refinements.
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Research details
- Subjects
- Mathematics · Combinatorics and Graph Theory
- Keywords
- partially ordered sets, linear extensions, balance, incomparability degree, local comparison counting
- Manuscript date
- 2026-10-20
- Reader reuse
- No additional permission granted
Scope
Uniform linear extensions of finite posets with bounded maximum incomparability degree; conditioned comparison probabilities, a range-dependent balance refinement, and a rare-triple obstruction.
Disclosures
AI tools assisted proof exploration, literature review, verification-code development and manuscript preparation.
Reproduction
The publication package contains the complete seven-page article, LaTeX source, a standard-library Python checker, expected scientific results, reader instructions, citation metadata, and file checksums.