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Subgroup Lattices and Symmetric Functions
Lynne M. Butler

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$45
Individual Members: US$27
Institutional Members: US$36
Order Code: MEMO/112/539
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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 Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.


Research mathematicians.

Table of Contents

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