I am attending a course on combinatorics. I was asked to present Möbius functions on lattices for this course. I was trying to look for a simple non-trivial problem that illustrates the need for lattice theory. All the standard texts define posets, lattices and get into proving theorems about different lattices and their ideal structures and so on. However I could'nt find a simple problem that was illuminating when viewed from the lattice viewpoint.

Other than the standard application of Möbius functions to divisors and cardinalities of sets, is there a simple problem (a puzzle would be even better!) that I can use to motivate Möbius functions on lattices?

Thank you

  • 3
    $\begingroup$ A nice reference list can be found at the end of this blog post. Vijay Garg's "Lattice Theory with Applications" is good for practical application of lattice theory. For your specific question, "Combinatorics: The Rota Way" will be more helpful. Möbius functions just require posets, but if you restrict yourself to (semi)lattices, things like the "Lindström–Wilf determinantal formula" become available. But I don't see the point to advertise Möbius functions on lattices instead of Möbius functions on posets. $\endgroup$ Apr 26, 2013 at 8:31
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    $\begingroup$ @thomas-klimpel What about converting your comment into an answer? $\endgroup$
    – J.-E. Pin
    Mar 15, 2015 at 14:38


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