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Subgroup Lattices and Symmetric Functions by Lynne M Butler; American Mathematical Society is a nonfiction available to read on EtoBox.

What is Subgroup Lattices and Symmetric Functions about?

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.

Who reads Subgroup Lattices and Symmetric Functions?

Author

Lynne M Butler; American Mathematical Society

Publisher

American Mathematical Society

Published

1994

Language

EN

ISBN

9780821826003

Category

nonfiction

Subjects

Mathematics, History, Science