A proof-heavy, open-access graduate textbook on algebraic combinatorics, including a full proof of the Littlewood-Richardson rule.
Determinants of weighted path matrices
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abstract
We find rational expressions for all minors of the weighted path matrix of a directed graph, generalizing the classical Lindstrom/Gessel-Viennot result for acyclic directed graphs. The formulas are given in terms of certain flows in the graph.
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An Introduction to Algebraic Combinatorics
A proof-heavy, open-access graduate textbook on algebraic combinatorics, including a full proof of the Littlewood-Richardson rule.