bibkey: lafreniere2025intervalclosed authors: Nadia Lafrenière, Joel Brewster Lewis, Erin McNicholas, Jessica Striker, Amanda Welch year: 2025 title: “Interval-closed set rowmotion and homomesy on products of two chains” doi: 10.48550/arXiv.2505.04000 url: https://arxiv.org/abs/2505.04000v1 claim: “Conjecture 4.2 restates the max-minus-min homomesy conjecture from the earlier interval-closed-set rowmotion paper for products of two chains; the paper proves a separate signed-cardinality result.” strata_touched:
- D5/S3/Combinatorics/Geometry/RectangleRowmotionHomomesy
- D5/S3/Combinatorics/Geometry/IntervalClosedSignedCardinalityRefutation license: citation-only triage: anchor
Interval-closed set rowmotion and homomesy on products of two chains
The follow-up studies interval-closed rowmotion and its orbits on products of two chains. Conjecture 4.2 explicitly cites the earlier max-minus-min homomesy conjecture. Its separate signed-cardinality homomesy theorem is not used as the target of the repository result.
Verified locator
- DOI: https://doi.org/10.48550/arXiv.2505.04000
- URL: https://arxiv.org/abs/2505.04000v1
- Version and location: arXiv:2505.04000v1, Conjecture 4.2 and Remark 4.3.
Signed-cardinality scope
Theorem 1.3 proves the m = 2 clause for odd n. Remark 3.31 (p. 40) retains the m = 3 clause in the sentence: “As noted in [11, Conjecture 4.12], the signed cardinality statistics seems to be homomesic under rowmotion for [3]×[n] when n is even.” The [3]×[12] refutation concerns that conjectural clause; it does not negate the proved two-row result.