On the Möbius Function of a Pointed Graded Lattice

Samuel Asefa Fufa () and Melkamu Zeleke ()
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Samuel Asefa Fufa: Addis Ababa University
Melkamu Zeleke: William Paterson University

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 1, 51-69

Abstract: Abstract In this paper, we compute the Möbius function of pointed integer partition and pointed ordered set partition using topological and analytic methods. We show that the associated order complex is a wedge of spheres and compute the associated reduced homology group for each subposet. In addition, we compute the Möbius function of pointed graded lattice and use our method to compute the Möbius function of pointed direct sum decomposition of vector spaces.

Keywords: Partition; pointed partition; Möbius function; poset map; simplicial complex; cone; contractible; homology group; simplicial map (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0255-x

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