Monthly Archives: March 2011

Algebraic combinatorics lecture 14: Polya Theory

We are given a domain , a finite set , and a group acting on , acting on . Let and , i.e., acts on , and splits it into orbits. Visually it’s easiest to represent as coloring schemes of … Continue reading

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Bi-invariant metrics on the symmetric groups, and a partial ordering on them

Persi asked me the other day to find other bi-invariant metrics on besides the Hamming metric and the Cayley metric. A metric on a group is called bi-invariant if for any . It is necessarily of the form where is … Continue reading

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Algebraic combinatorics Lecture 12: Dehn-Sommerville, flag enumeration and Eulerian posets; the tip of a convex iceberg

Let Q be a convex polytope in , and let be the number of i-dimensional faces. How are the related? Of course Euler’s relation states and for convex polytope, the genus is . Thus for , we can parametrize all … Continue reading

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