bibkey: leadertan2026triangulations
authors: Imre Leader, Ta Sheng Tan
year: 2026
title: "Some results on intersecting families of triangulations"
doi: null
url: https://arxiv.org/abs/2610.39116v1
claim: "Theorem 2 uses one-to-two ear compression; the proof of Lemma 8 applies the same compression to two cross-intersecting triangulation families with their common completion weight."
strata_touched:
  - D5/S3/Combinatorics/SetFamily/SimultaneousCompression
license: citation-only
triage: anchor

Ear compression and cross-intersection

Verified locator

URL: https://arxiv.org/abs/2610.39116v1

Full text: https://arxiv.org/html/2610.39116v1

The general case in the proof of Theorem 2 replaces a selected ear trace by its shifted trace and a feasible extension. The proof of Lemma 8 applies the same compression to two cross-intersecting families and inducts on the number of crossing pairs of observed ears; it explicitly omits the repeated compression details.

The paper’s triangulation families use a common completion weight. The repository’s abstract local theorem instead assumes separate one-to-two equations for two arbitrary nonnegative weights. Its iteration also requires exact projection images and both marginal equations on every reduced support. These are additional explicitly stated data, not conditional counting facts supplied by this citation. The actual conditioned polygon realization and a same-original-family deficit do not follow from this citation alone. No publication-priority claim is made.