2024/04/30 by Yifeng Huang, Huang, Yifeng · 2 citations
Computer Science · Engineering · Mathematics · #05A15 #15A24 #20K30 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2404.19483
openalex publication_date 2024/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix counting problems, many of which are under active research. Using a general framework we formulate for such counting problems, we reduce some counting problems about commuting matries to problems about endomorphisms on all finite abelian p-groups. As an application, we count finite modules on some first examples of nonreduced curves over \mathbbFq. We also relate some classical and hard problems regarding commuting triples of matrices to a conjecture of Onn on counting conjugacy classes of the automorphism group of an arbitrary finite abelian p-group.