1. Subgroups of finite Abelian groups 2. Hall-Littlewood symmetric functions

Summary

This work presents foundational research on two approaches to studying subgroup lattices of finite abelian [italic]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. We complete Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, and discuss their monotonicity results and a conjecture on Macdonald's two-variable Kostka functions

Notes

"November 1994, volume 112."

Bibliography

Includes bibliographical references (pages 157-160)