Counting on Determinants
Arthur T. Benjamin, Harvey Mudd College
We demonstrate how determinants solve many interesting combinatorial
problems. Determinants count nonintersecting lattice paths, spanning
trees, and permutations with specified descent points. Elegant proofs
of these results are based on the definition of the determinant
and occasionally the principle of inclusion-exclusion. Applications to
Pascal's Triangle, Fibonacci numbers and Catalan numbers will also be
given.
This talk is based on joint work with Naiomi Cameron of Occidental
College.