Subgroup Lattices and Symmetric Functions

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Subgroup Lattices and Symmetric...

Subgroup Lattices and Symmetric Functions

Name: Subgroup Lattices and Symmetric Functions
ISBN: 9780821826003

Lynne M. Butler

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This work presents foundational research on two approaches to studying subgroup lattices of finite abelian $p$-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schutzenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.

Categorias:

Mathematics

Volume:

112

Ano:

1994

Editora:

American Mathematical Society

Idioma:

english

Páginas:

166