**Memoirs of the American Mathematical Society**

1994;
160 pp;
Softcover

MSC: Primary 05; 06; 11; 20;

Print ISBN: 978-0-8218-2600-3

Product Code: MEMO/112/539

List Price: $45.00

Individual Member Price: $27.00

**Electronic ISBN: 978-1-4704-0118-4
Product Code: MEMO/112/539.E**

List Price: $45.00

Individual Member Price: $27.00

# Subgroup Lattices and Symmetric Functions

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*Lynne M. Butler*

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.