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Algebra and Combinatorics Research Group

Seminar: Spring 2008, Fridays, Milner 317, 3:00–3:50 p.m.






 

March 28

Gregory Berkolaiko ( TAMU )

3:00-4:00

The number of inequivalent minimal factorizations of an n-cycle

Abstract: We will discuss an elementary proof of the formula for the number of factorizations of the cycle (1,2,3,..n) into a product of transpositions. The proof uses a bijection between the factorizations and ternary trees.

The bijection is easy to visualize, which allows for an easy generalization: counting factorizations into a_k cycles of length k, for a suitable vector (a_2, a_3, ...). Some harder generalizations will also be mentioned.

The problem arose in an applied context of semiclassical analysis of quantum transport through a chaotic cavity. Time permitting, I will give a short elementary explanation of the physics involved.






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