AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Subgroup Lattices and Symmetric Functions
Lynne M. Butler
SEARCH THIS BOOK:

Memoirs of the American Mathematical Society
1994; 160 pp; softcover
Volume: 112
ISBN-10: 0-8218-2600-X
ISBN-13: 978-0-8218-2600-3
List Price: US$42
Individual Members: US$25.20
Institutional Members: US$33.60
Order Code: MEMO/112/539
[Add Item]

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.

Readership

Research mathematicians.

Table of Contents

  • Introduction
  • Subgroups of finite Abelian groups
  • Hall-Littlewood symmetric functions
  • Some enumerative combinatorics
  • Some algebraic combinatorics
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia