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MATH 739:
Topics in Algebra: Combinatorics of symmetric and quasisymmetric functions (Spring 2007)
Instructor:
Louis Billera
Meeting
Time & Room
We will study the combinatorial properties of the rings of symmetric
and quasisymmetric functions, beginning with the treatment found in Chapter
7 of Stanley's "Enumerative Combinatorics, vol.2". From there
we will consider the use of quasisymmetric functions in the enumeration
theory of graded and Eulerian partially ordered sets. In particular,
we will consider P-partitions and enriched P-partitions, as well as the
relationship of the latter to enumeration in polytopes and spherical
complexes. As time and interest allows, we can discuss the theory of
combinatorial Hopf algebras, due originally to Aguiar, or the application
of Eulerian enumeration to the study of Kazhdan-Lusztig polynomials of
Bruhat intervals in Coxeter groups.
Prerequisites: Math 631 or Math 434. Knowledge of basic poset theory would be
helpful, but not essential.
Last modified:October 31, 2006
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