Möbius function: Difference between revisions

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In [[combinatorics]], every locally finite [[partially ordered set|poset]] is assigned an [[incidence algebra]]. One distinguished member of this algebra is that poset's "Möbius function". The classical Möbius function treated in this article is essentially equal to the Möbius function of the set of all positive integers partially ordered by [[divisor|divisibility]]. See the article on [[incidence algebra]]s for the precise definition and several examples of these general Möbius functions.

==Physics==

The Möbius function can be interpreted in physics, in the context of

a theory with a logarithmic energy spectrum, as the operator

(−1)^''F'' that distinguishes fermions and bosons.

The fact that μ(''n'') vanishes when ''n'' is not squarefree is

equivalent to the [[Pauli exclusion principle]]. This identification

allows for a [[supersymmetric]] interpretation of the

[[Möbius inversion formula]].

==External links==

* [http://www.maa.org/editorial/mathgames/mathgames_11_03_03.html Ed Pegg's Maths Games: The Möbius function (and squarefree numbers)]

* [http://mathworld.wolfram.com/MoebiusFunction.html MathWorld: Möbius function]

* SomeInformation furtheron applicationsthe connections between physics and of μ(''n'') as its physical interpretation, specifically treated as the operator (−1)^''F'' what is equivalent to the ''Pauli exclusion principle'': http://www.maths.ex.ac.uk/~mwatkins/zeta/wolfgasphysics.htm

* Sloane's [http://www.research.att.com/~njas/sequences/Seis.html On-Line Encyclopedia of Integer Sequences]