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Research Paper#Algebra, Representation Theory🔬 ResearchAnalyzed: Jan 3, 2026 15:39

Finiteness and Silting-Discreteness in Graded Gentle and Skew-Gentle Algebras

Published:Dec 30, 2025 16:13
1 min read
ArXiv

Analysis

This paper contributes to the understanding of representation theory of algebras, specifically focusing on gentle and skew-gentle algebras. It extends existing results on τ-tilting finiteness and characterizes silting-discreteness using geometric models (surfaces and orbifolds). The results are significant for researchers in algebra and related fields, providing new insights into the structure and properties of these algebras.
Reference

“A skew-gentle algebra is τ-tilting finite if and only if it is representation-finite.”

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Research Paper#Random Walks, Group Theory, Generating Functions🔬 ResearchAnalyzed: Jan 3, 2026 15:56

Finiteness of Transformation Groups in Multidimensional Orthant Walks

Published:Dec 30, 2025 06:56
1 min read
ArXiv

Analysis

This paper addresses a fundamental question in the study of random walks confined to multidimensional spaces. The finiteness of a specific group of transformations is crucial for applying techniques to compute generating functions, which are essential for analyzing these walks. The paper provides new results on characterizing the conditions under which this group is finite, offering valuable insights for researchers working on these types of problems. The complete characterization in 2D and the constraints on higher dimensions are significant contributions.
Reference

“The paper provides a complete characterization of the weight parameters that yield a finite group in two dimensions.”

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