Cohen-Macaulay types of subgroup lattices of finite abelianp-groups |
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Authors: | Hideaki Morita |
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Institution: | (1) Department of Mathematics, Faculty of Science, Hokkaido University, 060 Sapporo, Japan |
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Abstract: | For a minimal free resolution of a Stanley-Reisner ring constructed from the order complex of a modular lattice. T. Hibi showed that its last Betti number (called the Cohen-Macaulay type) is computed by means of the Möbius function of the given modular lattice. Using this result, we consider the Stanley-Reisner ring of the subgroup lattice of a finite abelianp-group associated with a given partition, and show that its Cohen-Macaulay type is a polynomial inp with integer coefficients. |
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