A multiplicative deformation of the Möbius function for the poset of partitions of a multiset
نویسندگان
چکیده
The Möbius function of a partially ordered set is a very convenient formalism for counting by inclusion-exclusion. An example of central importance is the partition lattice, namely the partial order by refinement on partitions of a set {1, . . . , n}. It seems quite natural to generalize this to partitions of a multiset, i.e. to allow repetition of the letters. However, the Möbius function is not nearly so well-behaved. We introduce a multiplicative deformation, denoted μ, for the Möbius function of the poset of partitions of a multiset and show that it possesses much more elegant formulas than the usual Möbius function in this case.
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