Möbius function

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Möbius function

[′mər·bē·əs ‚fəŋk·shən]
(mathematics)
The function μ of the positive integers where μ(1) = 1, μ(n) = (-1) r if n factors into r distinct primes, and μ(n) = 0 otherwise; also, μ(n) is the sum of the primitive n th roots of unity.
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We will now show that the language for the Mobius function of ordinary factor order is not regular.
The Mobius function [mu]p(v) is defined recursively on a poset P as the unique function satisfying
From the definition of a(n), the Euler's summation formula (see [4]) and the properties of the Mobius function, we can get
Recall the one-variable Mobius function of a poset, [mu]: P [right arrow] Z, is defined recursively by
of the constant 1 function is called the exponential analogue of the Mobius function and it is denoted by [[mu].
For any integer z [member of] C, a Fleck-type generalized Mobius function (cf.
He analyzes the relevance of algebraic structures to number theory in such topics as ordered fields, fields with valuation and other algebraic structures, the role of the Mobius function and of generating functions, semigroups and certain convolution algebras.
The inverse of the zeta function is called the mobius function of the power set of S.
A classical question about any combinatorially defined poset is what its Mobius function is.
Second, the subset expansion is a summation of Mobius function values over the lattice of graphs, ordered by inclusion of edge sets.
For any real number t > 1 and positive integer n, from the properties of the Mobius function [mu](n) ( See reference [3]):
Indeed, when the increasing flip graph is the Hasse diagram of the increasing flip poset, this poset is EL-shellable, and we can compute its Mobius function.