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Totally Compatible Structures on Incidence Algebra Radical

Published:Dec 31, 2025 14:17
1 min read
ArXiv

Analysis

This paper investigates the structure of the Jacobson radical of incidence algebras, specifically focusing on 'totally compatible structures'. The finding that these structures are generally non-proper is a key contribution, potentially impacting the understanding of algebraic properties within these specific mathematical structures. The research likely contributes to the field of algebra and order theory.
Reference

We show that such structures are in general non-proper.

Tropical Geometry for Sextic Curves

Published:Dec 30, 2025 15:04
1 min read
ArXiv

Analysis

This paper leverages tropical geometry to analyze and construct real space sextics, specifically focusing on their tritangent planes. The use of tropical methods offers a combinatorial approach to a classical problem, potentially simplifying the process of finding these planes. The paper's contribution lies in providing a method to build examples of real space sextics with a specific number of totally real tritangents (64 and 120), which is a significant result in algebraic geometry. The paper's focus on real algebraic geometry and arithmetic settings suggests a potential impact on related fields.
Reference

The paper builds examples of real space sextics with 64 and 120 totally real tritangents.

Discussion#AI👥 CommunityAnalyzed: Jan 3, 2026 17:03

Ask HN: Am I the only one here who can't stand HN's AI obsession?

Published:Jan 13, 2025 12:44
1 min read
Hacker News

Analysis

The article expresses the author's boredom and lack of interest in the recent surge of AI-related news and developments on Hacker News. The author acknowledges the excitement around generative AI but finds the broader benefits of AI uncompelling and the articles on HN as noise. The author is seeking to find others who share the same sentiment.
Reference

I can't really explain why, but I find the recent AI developments, articles and news stories totally boring and lame. I can understand why people get excited with generative AI that can transform a text into an image etc, but otherwise the benefits of so called AI are completely lost on me, and all those AI articles on HN are just noise to me.