Math 512C: Algebraic Combinatorics
Patricia Hersh
Winter 2001, Monday/Wednesday/Friday 10:30-11:20
Text: Enumerative Combinatorics, Vol. II, by Richard
Stanley.
Generating Functions (3 weeks)
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Interpretations for composition and exponentiation of generating functions
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Lagrange inversion
Symmetric Functions (3-4 weeks)
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Different bases and relationships among these bases
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Connection to representations of the symmetric group
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Combinatorial applications
Group Actions on Posets (2-3 weeks)
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Will discuss one or more current papers using symmetric function and poset
topology to study representations on poset homology (e.g., a paper of Sundaram
recognizing plethysm representations by identifying their associated symmetric
functions through recursions they satisfy).