A weighted Möbius function
Copyright policy )A weighted Möbius function
For a fixed odd prime $\ell$, we define a variant of the classical Möbius function on the poset of isomorphism classes of finite abelian $\ell$-groups, then we prove an analog of Hall's theorem on the vanishing of the Möbius function.
7 pages, new introduction, updated references
- Portland State University United States
discrete probability distributions, Arithmetic functions; related numbers; inversion formulas, Abelian functions, 20K01 (Primary), 05E15 (Secondary), Group Theory (math.GR), Discrete mathematics, Möbius function, Cohen-Lenstra heuristics, posets, FOS: Mathematics, Discrete Mathematics and Combinatorics, moments, Asymptotic results on arithmetic functions, Mathematics - Group Theory, Möbius functions
discrete probability distributions, Arithmetic functions; related numbers; inversion formulas, Abelian functions, 20K01 (Primary), 05E15 (Secondary), Group Theory (math.GR), Discrete mathematics, Möbius function, Cohen-Lenstra heuristics, posets, FOS: Mathematics, Discrete Mathematics and Combinatorics, moments, Asymptotic results on arithmetic functions, Mathematics - Group Theory, Möbius functions
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