Subgroup lattices and symmetric functions / Lynne M. Butler.

Format:

Book

Author/Creator:

Butler, Lynne M., 1955- author.

Contributor:

American Mathematical Society.

Series:

Memoirs of the American Mathematical Society ; Volume 112, Number 539.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 112, Number 539

Language:

English

Subjects (All):

Symmetric functions.

Finite groups.

Lattice theory.

Physical Description:

1 online resource (173 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1994.

Language Note:

English

Summary:

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 Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.

Contents:

""2.5 Nonnegativity of Kostka polynomials""""2.6 Monotonicity of Kostka polynomials""; ""2.7 Two variable Kostka functions""; ""Table 2""; ""A Some enumerative combinatorics""; ""A.1 Partitions and finite abelian groups""; ""B Some algebraic combinatorics""; ""B.1 Symmetric functions""; ""B.2 Tableau terminology""

Notes:

"November 1994, Volume 112, Number 539 (third of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0118-5