Exploring Generating Functions in Combinatorics
This chapter introduces the Matrix-Tree Theorem and shows how matrix determinants can be used to count spanning trees in graphs.
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Two Proofs of the Matrix-Tree Theorem
This chapter introduces the Matrix-Tree Theorem and presents two proofs, using induction and the Cauchy-Binet formula, to show how determinants can be used to count spanning trees in a graph.
Binomial Coefficients, Vandermonde Identity and Catalan Numbers
This note reviews several classical topics in combinatorics, including binomial coefficients, combinatorial identities, double counting, Vandermonde’s identity, and Catalan numbers, with an emphasis on combinatorial proofs and counting arguments.
CS229 Lecture 11
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CS229 Lecture 10
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CS229 Lecture 9
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CS229 Lecture 8
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CS229 Lecture 7
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