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Combinatorics by Peter J. Cameron

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12. Posets, lattices and matroids

good order and military discipline

Army regulations

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TOPICS: Posets, lattices; distributive lattices; (propositional logic); chains and antichains; product and dimension; Möbius inversion; matroids; (Arrow’s Theorem)

TECHNIQUES: Möbius inversion

ALGORITHMS: Calculating the Möbius function; minimum-weight basis

CROSS-REFERENCES: PIE (Chapter 5); Hall’s Theorem (Chapter 6); q-binomial theorem (Chapter 9)

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Order is fundamental to the process of measurement: representing objects by numbers presupposes that we can arrange ...

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