Preprint Mathematics
Local comparison counting for linear extensions and a bounded-range balance refinement
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Overview
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.
Keywords partially ordered sets · linear extensions · balance · incomparability degree · local comparison counting
Scope of the work
Uniform linear extensions of finite posets with bounded maximum incomparability degree; conditioned comparison probabilities, a range-dependent balance refinement, and a rare-triple obstruction.
Reproduction notes
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Scott Schubr. (2026). Local comparison counting for linear extensions and a bounded-range balance refinement (Version 1). Luminary Research Archive. https://luminaryoddities.com/researcharchive/local-comparison-counting-linear-extensions-bounded-range-balance-refinement/v/1
BibTeX
@techreport{luminary_local_comparison_counting_linear_extensions_bounded_range_balance_refinement_v1,
title = {Local comparison counting for linear extensions and a bounded-range balance refinement},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Preprint},
note = {Version 1},
url = {https://luminaryoddities.com/researcharchive/local-comparison-counting-linear-extensions-bounded-range-balance-refinement/v/1}
}Reader correspondence
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